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Algebraic analysis of infinite symmetry

Research Project

Project/Area Number 22340005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

KASHIWARA Masaki  京都大学, 数理解析研究所, 研究員 (60027381)

Co-Investigator(Renkei-kenkyūsha) ARIKI Susumu  大阪大学, 大学院情報科学研究科, 教授 (40212641)
TANISAKI Toshiyuki  大阪市立大学, 理学研究科, 教授 (70142916)
NAKASHIMA Toshiki  上智大学, 理工学部, 教授 (60243193)
KATO Syu  京都大学, 理学部, 准教授 (40456760)
MIWA Tetsuji  京都大学, 国際高等教育院, 特定教授 (10027386)
Research Collaborator SCHAPIRA Pierre  
KANG Seok-Jin  
VILONEN Kari  
D'AGNOLO Andrea  
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥15,340,000 (Direct Cost: ¥11,800,000、Indirect Cost: ¥3,540,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords表現論 / リーマン・ヒルベルト対応 / 圏化 / 量子群 / 箙ヘッケ環 / 不確定特異点ホロノミック系 / 国際研究者交流 / イタリア:フランス:アメリカ:韓国 / ワイル・シューア双対性 / 変形量子化 / 結晶基底 / 超局所解析
Outline of Final Research Achievements

There are three significant results of the research on representation theory during these five years.
First, I proved the Riemann-Hilbert correspondence for holonomic D-modules (with A. D'Agnolo). Second, I proved ``codimension-three conjecture''(with K. Vilonen). Third, I established a categorification of quantum groups via cyclotomic quiver Hecke algebras (with S-J. Kang).

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (30 results)

All 2014 2013 2012 2011 2010

All Journal Article (17 results) (of which Peer Reviewed: 17 results,  Open Access: 4 results,  Acknowledgement Compliant: 3 results) Presentation (12 results) (of which Invited: 8 results) Book (1 results)

  • [Journal Article] Supercategorification of quantum Kac-Moody algebras II.2014

    • Author(s)
      Kang, Seok-Jin; Kashiwara, Masaki; Oh, Se-jin
    • Journal Title

      Adv. Math.

      Volume: 265 Pages: 169-240

    • DOI

      10.1016/j.aim.2014.07.036

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Microdifferential systems and the codimension-three conjecture.2014

    • Author(s)
      Kashiwara, Masaki; Vilonen, Kari
    • Journal Title

      Ann. of Math. (2)

      Volume: 180 Issue: 2 Pages: 573-620

    • DOI

      10.4007/annals.2014.180.2.4

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Microlocal Euler classes and Hochschild homology.2014

    • Author(s)
      Kashiwara, Masaki; Schapira, Pierre
    • Journal Title

      J. Inst. Math. Jussieu

      Volume: 13 Issue: 3 Pages: 487-516

    • DOI

      10.1017/s1474748013000169

    • NAID

      120005456014

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux.2014

    • Author(s)
      Grantcharov, Dimitar; Jung, Ji Hye; Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 366 Issue: 1 Pages: 457-489

    • DOI

      10.1090/s0002-9947-2013-05866-7

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Categorification of highest weight modules2013

    • Author(s)
      Seok-Jin Kang, Masaki Kashiwara, Se-jin Oh,
    • Journal Title

      Mosc. Math. J.

      Volume: 13

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric realization of Khovanov-Lauda-Rouquier algebras2013

    • Author(s)
      Seok-Jin Kang, Masaki Kashiwara, Euiyong Park
    • Journal Title

      Proc. Lond. Math. Soc. (3)

      Volume: 107 Issue: 4 Pages: 907-931

    • DOI

      10.1112/plms/pds095

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Supercategorification of quantum Kac-Moody algebras2013

    • Author(s)
      Seok-Jin Kang, Masaki Kashiwara, Se-jin Oh
    • Journal Title

      Adv. Math.

      Volume: 242

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras2012

    • Author(s)
      Seok-Jin Kang, Masaki Kashiwara
    • Journal Title

      Invent. Math.

      Volume: 190 Issue: 3 Pages: 699-742

    • DOI

      10.1007/s00222-012-0388-1

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a reconstruction theorem for holonomic systems2012

    • Author(s)
      Andrea d'Agnolo, Masaki Kashiwara
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 88 Issue: 10

    • DOI

      10.3792/pjaa.88.178

    • NAID

      40019573004

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Biadjointness in cyclotomic Khovanov-Lauda-Rouquier algebras2012

    • Author(s)
      Masaki Kashiwara
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: 48 Issue: 3 Pages: 501-524

    • DOI

      10.2977/prims/78

    • NAID

      110009487559

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras2012

    • Author(s)
      Seok-Jin Kang, Masaki Kashiwara, Olivier Schiffmann
    • Journal Title

      Math. Ann.

      Volume: 354 Issue: 1 Pages: 193-208

    • DOI

      10.1007/s00208-011-0725-5

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Notes on parameters of quiver Hecke algebras2012

    • Author(s)
      Masaki Kashiwara
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 88 Issue: 7

    • DOI

      10.3792/pjaa.88.97

    • NAID

      40019357218

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems2012

    • Author(s)
      Stephane Guillermou, Masaki Kashiwara, Pierre Schapira
    • Journal Title

      Duke Math. J.

      Volume: 161 Issue: 2

    • DOI

      10.1215/00127094-1507367

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On quantization of complex symplectic manifolds2011

    • Author(s)
      Andrea D'Agnolo, Masaki Kashiwara
    • Journal Title

      Comm.Math.Phys.

      Volume: 308 Issue: 1 Pages: 81-113

    • DOI

      10.1007/s00220-011-1325-7

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum queer superalgebra and crystal bases2010

    • Author(s)
      Grantcharov, Dimitar; Jung, JiHye; Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci.

      Volume: 86 Pages: 177-182

    • NAID

      40017436331

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the co dimension-three conjecture2010

    • Author(s)
      Kashiwara, Masaki; Vilonen, Kari
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci.

      Volume: 86 Pages: 154-158

    • NAID

      40017436326

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tropical R maps and affine geometric crystals2010

    • Author(s)
      Kashiwara, Masaki; Nakashima, Toshiki; Okado, Masato
    • Journal Title

      Represent.Theory

      Volume: 14 Pages: 446-509

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Monoidal Categorifications of cluster algebras2014

    • Author(s)
      柏原 正樹
    • Organizer
      Cluster algebras and Representation theory
    • Place of Presentation
      Seoul (韓国)
    • Year and Date
      2014-11-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Simplicity of heads and socles of tensor products2014

    • Author(s)
      柏原 正樹
    • Organizer
      Representation theory and related topics
    • Place of Presentation
      Daegu (韓国)
    • Year and Date
      2014-08-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Riemann-Hilebert correspondence of irregular holonomic D-modules2014

    • Author(s)
      柏原 正樹
    • Organizer
      Combinatorial Representation theory
    • Place of Presentation
      Montreal (Cannada)
    • Year and Date
      2014-05-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Parameters of quiver Hecke algebras2014

    • Author(s)
      柏原 正樹
    • Organizer
      Combinatorial Representation theory
    • Place of Presentation
      Montreal (Cannada)
    • Year and Date
      2014-05-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Symmetric quiver Hecke algebras and R-matrix2014

    • Author(s)
      柏原 正樹
    • Organizer
      Combinatorial Representation theory
    • Place of Presentation
      Montreal (Cannada)
    • Year and Date
      2014-04-21
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Riemann-Hilbert correspondence for irregular holonomic D-modules2013

    • Author(s)
      柏原正樹
    • Organizer
      SNU colloquium
    • Place of Presentation
      Seoul Natiuonal University, Seoul、韓国
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Categorical representation theory2012

    • Author(s)
      柏原正樹
    • Organizer
      SNU colloquium
    • Place of Presentation
      Seoul Natiuonal University, Seoul、韓国
    • Related Report
      2012 Annual Research Report
  • [Presentation] Categorification of quantam algebras via quiver Hecke algebras2012

    • Author(s)
      柏原正樹
    • Organizer
      Category O: geometrie et categorification
    • Place of Presentation
      Centre International de Rencontres Mathematiques, (Marseille, France)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] KLR algebras and R-matrices of quantum affine algebras2012

    • Author(s)
      柏原正樹
    • Organizer
      Seminaire d'Algebre
    • Place of Presentation
      Institut de Henri Poincare (Paris, France)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Cyclotomic quiver Hecke algebras and Categorification of quantum groups2011

    • Author(s)
      柏原正樹
    • Organizer
      KAIST colloquium
    • Place of Presentation
      KAIST, Daejon、韓国
    • Year and Date
      2011-06-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Crysytal bases of the quantized queer super-algebra2010

    • Author(s)
      Masaki Kashiwara
    • Organizer
      Algebraic and Conbinatorial approach to representation theory
    • Place of Presentation
      International Centre for theoretical Science, Bangalore, India
    • Year and Date
      2010-08-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] The ring of differential operators and its invariants2010

    • Author(s)
      Masaki Kashiwara
    • Organizer
      Workshop and International Conference on Representation of Algebras (ICRAXIV)
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Related Report
      2010 Annual Research Report
  • [Book] Deformation quantization modules2012

    • Author(s)
      Masaki Kashiwara, Pierre Schapira
    • Total Pages
      159
    • Publisher
      Ast'erisque, No. 345, Soc. Math. France
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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