Updated on 2025/03/28

写真a

 
KANNO, Hiroaki
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor

Degree 1

  1. Doctor of Science ( Kyoto University ) 

Research Areas 2

  1. Others / Others  / Elementary Particle/Atomic Nucleus/Cosmic Ray/Space Physics

  2. Others / Others  / Geometry

Current Research Project and SDGs 1

  1. Topological Quantum Field Theory

Education 2

  1. Kyoto University   Graduate School, Division of Natural Science

    - 1989

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    Country: Japan

  2. Kyoto University   Faculty of Science

    - 1984

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    Country: Japan

Professional Memberships 2

  1. 日本物理学会

  2. 日本数学会

 

Papers 54

  1. Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation

    Awata, H; Hasegawa, K; Kanno, H; Ohkawa, R; Shakirov, S; Shiraishi, J; Yamada, Y

    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS   Vol. 20   2024

  2. Solitons in open N=2 string theory

    Hamanaka, M; Huang, SC; Kanno, H

    PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS   Vol. 2023 ( 4 )   2023.4

  3. Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painleve<acute accent> Equation

    Awata, H; Hasegawa, K; Kanno, H; Ohkawa, R; Shakirov, S; Shiraishi, J; Yamada, Y

    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS   Vol. 19   2023

  4. Quasi-Hopf twist and elliptic Nekrasov factor

    Cheewaphutthisakun, P; Kanno, H

    JOURNAL OF HIGH ENERGY PHYSICS   ( 12 )   2021.12

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    Language:Japanese  

    DOI: 10.1007/JHEP12(2021)130

    Web of Science

  5. MacMahon KZ equation for Ding-Iohara-Miki algebra

    Cheewaphutthisakun, P; Kanno, H

    JOURNAL OF HIGH ENERGY PHYSICS   ( 4 )   2021.4

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    Language:Japanese  

    DOI: 10.1007/JHEP04(2021)031

    Web of Science

  6. Quiver matrix model of ADHM type and BPS state counting in diverse dimensions

    Kanno, H

    PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS   Vol. 2020 ( 11 )   2020.11

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    Language:Japanese  

    DOI: 10.1093/ptep/ptaa079

    Web of Science

  7. Shiraishi functor and non-Kerov deformation of Macdonald polynomials

    Awata, H; Kanno, H; Mironov, A; Morozov, A

    EUROPEAN PHYSICAL JOURNAL C   Vol. 80 ( 10 )   2020.10

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  8. Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei

    JOURNAL OF HIGH ENERGY PHYSICS   ( 8 )   2020.8

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/JHEP08(2020)150

    Web of Science

  9. On a complete solution of the quantum Dell system

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei

    JOURNAL OF HIGH ENERGY PHYSICS   ( 4 )   2020.4

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/JHEP04(2020)212

    Web of Science

  10. Can tangle calculus be applicable to hyperpolynomials?

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei

    NUCLEAR PHYSICS B   Vol. 949   2019.12

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.nuclphysb.2019.114816

    Web of Science

  11. The MacMahon R-matrix

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Suetake Kazuma, Zenkevich Yegor

    JOURNAL OF HIGH ENERGY PHYSICS   ( 4 )   2019.4

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/JHEP04(2019)097

    Web of Science

  12. Equivariant U(N) Verlinde algebra from Bethe/gauge correspondence

    Kanno Hiroaki, Sugiyama Katsuyuki, Yoshida Yutaka

    JOURNAL OF HIGH ENERGY PHYSICS   ( 2 )   2019.2

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/JHEP02(2019)097

    Web of Science

  13. Nontorus link from topological vertex

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey

    PHYSICAL REVIEW D   Vol. 98 ( 4 )   2018.8

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    DOI: 10.1103/PhysRevD.98.046018

    Web of Science

  14. (q,t)-KZ Equations for quantum toroidal algebra and Nekrasov partition function on ALE spaces Reviewed

    H.Awata, H.Kanno, A.Mironov, A.Morozov, K.Suetake and Y.Zenkevich

    Journal of High Energy Physics   Vol. 1803 ( 3 )   2018.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/JHEP03(2018)192

    Web of Science

  15. Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor

    PHYSICAL REVIEW D   Vol. 96 ( 2 )   2017.7

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    DOI: 10.1103/PhysRevD.96.026021

    Web of Science

  16. Anomaly in RTT relation for DIM algebra and network matrix models

    Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor

    NUCLEAR PHYSICS B   Vol. 918   page: 358 - 385   2017.5

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.nuclphysb.2017.03.003

    Web of Science

  17. Anomaly in RTT relation for DIM algebra and Network Matrix Models Reviewed

    H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich

    Nuclear Physics B   Vol. 918   page: 358-385   2017.3

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  18. Generalized Knizhnik-Zamolodchikov Equation for Ding-Iohara-Miki algebra, Reviewed

    H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich

    Phys. Rev. D   Vol. 96   page: 026021   2017

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  19. Toric Calabi-Yau manifolds as Quantum Integrable Systems; R-matrix and RTT relations

    H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich

    Journal of High Energy Physics   Vol. 1610   page: 047   2016.10

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  20. Explicit Examples of DIM Constraints for Network Matrix Models Reviewed

    H.Awata, H.Kanno, T.Matsumoto, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich

    Journal of High Energy Physics   Vol. 1607   page: 103   2016.7

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  21. Hyperkaehler Metrics from Monopole Walls Reviewed

    M.Hamanaka, H.Kanno and D.Muranaka

    Phys. Rev.   Vol. D 89   2014.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1103/PhysRevD.89.065033

  22. W_3 irregular states and isolated N=2 superconformal field theories Reviewed

    H.Kanno, K.Maruyoshi, S.Shiba and M.Taki

    Journal of High Energy Physics   Vol. 1303   page: 147   2013.3

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  23. Changing the preferred direction of the refined topological vertex Reviewed

    H.Awata and H.Kanno

    Journal of Geometry and Physics   Vol. 64   page: 91-110   2013

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  24. Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String Reviewed

    H.Awata, H.Fuji, H.Kanno, M.Manabe and Y.Yamada

    Advances in Theoretical and Mathematical Physics   Vol. 16 ( 3 ) page: 725 - 804   2012.6

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  25. Generalized Whittaker states for instanton counting with fundamental hypermultiplets Reviewed

    H.Kanno and M.Taki

    Journal of High Energy Physics   Vol. 1205   page: 052   2012.5

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  26. Instanton counting with a surface operator and the chain-saw quiver

    H.Kanno, and Y.Tachikawa

    Journal of High Energy Physics   Vol. 11 ( 06 ) page: 119   2011.6

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  27. Macdonald operators and homological invariants of the colored Hopf link Reviewed

    H.Awata and H.Kanno

    J. Phys. A: Math. Theor.   Vol. 44   page: 375201   2011

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  28. Quiver matrix model and and topological partition function in six dimensions Reviewed

    H.Awata and H.Kanno

    Journal of High Energy Physics   Vol. 9 ( 7 ) page: 076   2009.7

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  29. Refined BPS state counting from Nekrasov's formula and Macdonald functions Reviewed

    H.Awata and H.Kanno

    International Journal of Modern Physics A   Vol. 24 ( 12 ) page: 2253-2306   2009

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  30. Instanton Counting and the Chiral Ring Relations in Supersymmetric Gauge Theories Reviewed

    H.Kanno

    Adv. Stud. Pure Math.   Vol. 55   page: 51-67   2009

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  31. Instanton Calculus and Chiral One-point Functions in Supersymmetric Gauge Theories Reviewed

    S.Fujii, H.Kanno, S.Moriyama and S.Okada

    Adv. Theor. Math. Phys.   Vol. 12   page: 1401-1428   2008

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  32. Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory Reviewed

    H.Kanno and S.Moriyama

    Phys. Rev.D   Vol. 77   page: 126001   2008

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  33. Universal Character and Large N Factorizationin Topological Gauge/String Theory Reviewed

    H.Kanno

    Nuclear Physics   Vol. B745 [PM]   page: 165-175   2006

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  34. Instanton counting, Macdonald function and the moduli space of D-branes Reviewed

    H.Awata and H.Kanno

    Journal of High Energy Physics   Vol. 5   page: 039   2005

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  35. Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes Reviewed

    T.Eguchi and H.Kanno

    Physics Letters   Vol. B585   page: 163-172   2004

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  36. Whitham Prepotential and Superpotential Reviewed

    H.Itoyama and H.Kanno

    Nuclear Physics   Vol. B686   page: 155-164   2004

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  37. *Topological Strings and Nekrasov's Formulas Reviewed

    T.Eguchi and H.Kanno

    Journal of High Energy Physics   Vol. 12   page: 006   2003

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  38. Supereigenvalue Model and Dijkgraaf-Vafa Proposal Reviewed

    H.Itoyama and H.Kanno

    Physics Letters   Vol. B573   page: 227-234   2003

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  39. On Spin(7) Holonomy Metric Based on SU(3)/U(1) II Reviewed

    H.Kanno and Y.Yasui

    Journal of Geometry and Physics   Vol. 43   page: 310-326   2002

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  40. On Spin(7) Holonomy Metric Based on SU(3)/U(1) Reviewed

    H.Kanno and Y.Yasui

    Journal of Geometry and Physics   Vol. 43   page: 293-309   2002

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  41. Octonionic Yang-Mills instanton on quaternionic line bundle of Spin(7) holonomy

    H.Kanno and Y.Yasui

    Journal of Geometry and Physics   Vol. 34   page: 302   2000

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  42. Five-Dimensional Gauge Theories and Local Mirror Symmetry Reviewed

    T.Eguchi and H.Kanno

    Nuclear Physics   Vol. B586   page: 331   2000

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  43. *Special Quantum Field Theories in Eight and Other Dimensions Reviewed

    L.Baulieu, H.Kanno and I.M.Singer

    Communications in Mathematical Physics   Vol. 194   page: 149   1998

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  44. Donaldson-Witten functions of massless N=2 supersymmetric QCD

    H.Kanno and S.-K.Yang

    Nuclear Physics   Vol. B535   page: 512   1998

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  45. Picard-Fuchs equation and prepotential of five-dimensional SUSY gauge theory compactified on a circle

    Nuclear Physics   Vol. B530   page: 73   1998

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  46. Two-toroidal Lie Algebra as Current Algebra of Four-dimensional Kaehler WZW Model Reviewed

    T.Inami, H.Kanno, T.Ueno and C.S.Xiong

    Physics Letters   Vol. B399   page: 97   1997

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  47. Topological strings with scaling violation and Toda lattice hierarchy Reviewed

    H.Kanno and Y.Ohta

    Nuclear Physics   Vol. B442   page: 179   1995

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  48. BRST cohomology ring in 2D gravity coupled to minimal models

    H.Kanno and M.H.Sarmadi

    International Journal of Modern Physics   Vol. A9   page: 39   1994

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  49. Toda lattice hierarchy and the topological description of the c=1 string theory

    T.Eguchi and H.Kanno

    Physics Letters   Vol. B331   page: 330   1994

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  50. Woo algebra in a two-dimensional black hole Reviewed

    T.Eguchi, H.Kanno and S.-K.Yang

    Physics Letters B   Vol. 298   page: 73   1993

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  51. Topological strings, flat coordinates and gravitational descendants Reviewed

    T.Eguchi, H.Kanno, Y.Yamada and S.-K.Yang

    Physics Letters B   Vol. 305   page: 235   1993

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  52. SO(2, C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter Reviewed

    N.Chair, V.K.Dobrev and H.Kanno

    Physics Letters B   Vol. 283   page: 194   1992

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  53. *Lie superalgebraic approach to super Toda lattice and gereralized super KdV Equations Reviewed

    T.Inami and H.Kanno

    Communications in Mathematical Physics   Vol. 136   page: 519   1991

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  54. *Weil algebra structure and geometrical meaning of BRST transformation in topological guantum field theory Reviewed

    Zeitschrift fur Physik C   Vol. 43   page: 477   1989

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▼display all

Books 1

  1. BRS Cohomology in Topological String Theory and Integrable Systems

    BRS Symmetry  1996 

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    Language:English

Research Project for Joint Research, Competitive Funding, etc. 1

  1. ゲージ・重力理論対応と可積分系

    2008.10 - 2010.3

    大幸財団 

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    Grant type:Competitive

KAKENHI (Grants-in-Aid for Scientific Research) 5

  1. 二重楕円型量子可積分系と枠付き放物層の数え上げ

    Grant number:23K03087  2023.4 - 2027.3

    科学研究費助成事業  基盤研究(C)

    菅野 浩明

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    Authorship:Principal investigator 

    Grant amount:\2860000 ( Direct Cost: \2200000 、 Indirect Cost:\660000 )

    座標と運動量がともに二重周期性を持つ可積分系である二重楕円型可積分系について,超対称ゲージ理論との対応関係を通して,その性質を明らかにする.互いに可換なハミルトニアンの同時固有関数は,対応する超対称ゲージ理論側で枠付き放物層の数え上げに関する分配関数で与えられると予想されている.楕円量子群の表現論を用いて,分配関数を絡み作用素の同変指標として書き換えることにより,分配関数の満たす差分方程式を求める.また二重楕円型可積分系は座標と運動量の入れ替えに関して自己双対性をもつことが期待されている.分配関数のもつ対称性を明らかにすることによって自己双対性が実現されていることを示す.
    2次元共形場理論の共形ブロックは Virasoro 代数の表現論において基本的な役割を果たすが,変形 Virasoro 代数の共形ブロックの数学的定義は,まだ与えられていない.5次元版の AGT 対応は面欠陥付きの K 理論的 Nekrasov 分配関数と変形 Virasoro 代数の共形ブロックの対応を予想するので,このような Nekrasov 分配関数を変形 Virasoro 代数の共形ブロックとみなして,その性質を調べるという立場が可能である.面欠陥付きの Nekrasov 分配関数は,幾何学的には放物層の数え上げにより定義される.
    近年 Sh.Shakirov 氏は,このような分配関数に対する,新しいタイプの非定常差分方程式 (Shakirov 方程式)を発見した.この非定常差分方程式は有理曲線上の共形ブロックに対する BPZ 方程式の量子変形版とみなすことができる.一方で BPZ 方程式はパンルヴェ方程式やカレント代数の共形ブロックに対する Knizhnik-Zamolodchikov (KZ) 方程式と対応することが知られている.我々は,適切なゲージ変換を用いて Shakirov 方程式を書き換えることにより,この方程式が VI 型の非定常離散パンルヴェ方程式の量子化となっていることを明らかにした.VI 型離散パンルヴェ方程式の時間発展はアフィン Kac-Moody 代数 D_5^{(1)} の拡大アフィンワイル群の適切な並進元によって定義される.この並進元を非可換な(量子化された)力学変数の空間上で表現したものが Shakirov 方程式のハミルトニアンとなっている.
    枠付き放物層の数え上げから定義される K 理論的 Nekrasov 分配関数が満たす非定常差分方程式が量子化された離散パンルヴェ方程式と見なされることが示されたことは,放物層の数え上げと量子可積分系の関係に関する新たな展望を開くものである.また変形 Virasoro 代数の共形ブロックとの関係についても次のような意味から興味深い.表現論的に変形 Virasoro 代数の取り扱いが難しい理由の一つは,余積が定義できないため量子群とならないことであった.パンルヴェ方程式の量子化は,モノドロミー保存変形の立場からアフィン量子代数の表現論で重要な役割をはたす量子 KZ 方程式と結びつく.したがって今年度得られた結果は,変形 Virasoro 代数の共形ブロックに対する表現論的アプローチに道を開くものである.本研究課題は楕円型可積分系に関するものであるので,以上の結果を楕円 Virasoro 代数へ拡張することは今後の課題である.
    ここまでの研究では楕円型量子可積分系に関する課題に進展がなかった.離散パンルヴェ方程式には楕円型の拡張も存在するので,今年度の研究成果が楕円型に拡張できるか検討を行う.また K 理論的 Nekrasov 分配関数の観点から,楕円型への拡張を行うためには随伴表現に従う物質場を考える必要があり,これにはパンルヴェ方程式を超えた世界を考えることが必要となる可能性がある.一方で,今年度の成果から派生する新たな課題として,ゲージ群のランクが高い場合への拡張も視野に入れて研究を進める予定である.

  2. Difference equations associated with quantum toroidal algebra and hyper-Kaehler quotient

    Grant number:18K03274  2018.4 - 2024.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Kanno Hiroaki

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    Authorship:Principal investigator 

    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    We have derived difference equations of KZ type for the correlation functions or the trace of the products of intertwining operators of the quantum toroidal algebra of type gl_1. We also investigated the structure of solutions and clarified the relation to the Nekrasov partition function of elliptic type. We have investigated the non-stationary difference equation for the K-theoretic Nekrasov partition function with a surface defect, which we can regard as a conformal block of the deformed Virasoro algebra. We have proved that by gauge
    transformation the equation is transformed to a quantized version of discrete Painreve VI equation. The underlying moduli space is the affine Laumon space, which is only Kaehler quotient. In this sense this equation belongs to a new class of difference equations which was not expected in the beginning of the project.

  3. Research of lattices, automorphic forms and moduli spaces

    Grant number:15H05738  2015.5 - 2020.3

    Kondo Shigeyuki

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    Authorship:Coinvestigator(s) 

    We studied symmetries of manifolds from a wide-angle. We obtained a complete classification of Enriques surfaces with finite automorphism group and results on automorphisms of K3 and Enriques surfaces related with complex dynamical systems, and discovered a new phenomenon of Enriques surfaces by using the theory of a famous lattice, called Leech lattice, in sphere packing problem. And we studied moduli problems. In particular, we determined an important invariant, called the Kodaira dimensions, of some moduli spaces by applying the theory of automorphic forms. We also obtained several results related with Mathematical Physics and representation theory, for example, a duality phenomenon in Mathieu moonshine.

  4. M ブレインと量子可積分系

    2012.4

    科学研究費補助金  基盤研究(C)

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  5. 弦双対性が予言するアクセサリパラメータ付き特殊関数

    2007 - 2009

    科学研究費補助金  萌芽研究,課題番号:19654007

    菅野 浩明

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Teaching Experience (On-campus) 1

  1. Linear Algebra II

    2011