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Representation theory of algebraic groups through algebraic analysis

Research Project

Project/Area Number 11440009
Research Category

Grant-in-Aid for Scientific Research (B).

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

Principal Investigator

TANISAKI Toshiyuki  Hiroshima Univ., Graduate school of Science, Professor, 大学院・理学研究科, 教授 (70142916)

Co-Investigator(Kenkyū-buntansha) SHOJI Toshiaki  Tokyo Science Univ., Faculty of Science and Engineering, Professor, 理工学部, 教授 (40120191)
KASHIWARA Masaki  Kyoto Univ., Research Institute of Natheuatical Science, Professor, 数理解析研究所, 教授 (60027381)
SAITO Yashihisa  Hiroshima Univ., Graduate school of Science, Assistant, 大学院・理学研究科, 助手 (20294522)
KAWANAKA Norkki  Osaka Univ., Graduate School of Science, Professor, 理学研究科, 教授 (10028219)
KANEDA Masahara  Osaka City Univ., Faculty of Science, Professor, 理学部, 教授 (60204575)
竹内 潔  筑波大学, 数学系, 講師 (70281160)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥9,100,000 (Direct Cost: ¥9,100,000)
Fiscal Year 2000: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 1999: ¥5,200,000 (Direct Cost: ¥5,200,000)
Keywordsalgebraic group / representation / algebraic analysis / カッツムーディ・リー代数 / 最高ウェイト加群 / 量子群
Research Abstract

1. Highest weight modules over Kac-Moody Lie algebras
Kashiwara and Tanisaki tried to determine characters of irreducible modules over affine Lie algebras with critical highest weights. In particular, they considered relations of representations of affine Lie algebras with D-modules on the semi-infinite flag manifold. Through the investigation they noticed that the behavior of the equivariant line bundles is quite different from those on the ordinary flag manifold.
2. Flag manifold for quantum groups
Tanisaki constructed generalized flag manifold corresponding to general parabolic subgroups. The treatment of the unipotent radical is more delicate than the ordinary case. Besides Morita and Tanisaki tried to find a good formulation for the sheaf cohomologies and D-modules on the quantized flag manifold from the view point of non-commutative schemes.
3. Representations of toroidal Lie algebras
Saito constructed certain representations of toroidal Lie algebras usig Boson. He also investigated the automorphisms of the toroidal Lie algebras and found a connection with the moudular groups.
4. Representations of quantum groups over Laurent polynimial rings
Kaneda investigated representations of quantum groups over the Laurent polynimial rings, and have proved a version of a theorem of Kempf.
5. Solvable games
Kawanaka found a generalization of Sato's game, and investigated on it from the view point of representation theory.
6..Representations of comples reflection groups and their Hecke algebras
Shoji tried to extend the Frobenius formua for the Hecke algebra of type A to the Hecke algebras for complex reflection groups, and succeed in it in the case of Ariki-Koike algebra.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] M.Kashiwara: "Characters of irreducible models with non-critical highest weights over affine Lie algebras"Proc.International conference on representation theory. 275-296 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kashiwara: "Parabolic Kazhdan-Lusztig pdynonials and Schubert varieties"J.Algebra. (in press). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Kawanake: "A q-Cauchy idutity for Schur functions and umprimitive complex veffection groups"Osaka J.Math. (in press). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Shoji: "A Frobenius formula for the characters of Ariki-Koike algebras"Beitrage zur Algebra and Geometne. 41. 115-140 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Shoji: "Length functions of G(r,p,n)"Advanced Studies in Pure Math.. 28. 327-342 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kaneda: "Cohomology of infinitesimal quantum algebras"J.Algebra. 226. 818-856 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 柏原正樹: "代数解析概論"岩波書店. 250 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kashiwara: "Characters of irreducible modules with non-critical highest weights over attire Lie algebras."Proc.International conference on representation theory. 275-296 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kashiwara: "Parabolic Kazhdan-Lusztig polynamids and Schubert varieties"J Algebra. (in press). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Kawanaka: "A q-Canchy icentity for Schur functions and imprimitive complex reflection groups"Osaka J.Math. (in press). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Shoji: "A-Frobenius formula for the characters of Ariki-Koike algebras"Beitrage zur Algebra und Geowerie. 41. 115-140 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Shoji: "Length function of G (r, r, m)"Advanced Studies in pure Math. 28. 327-342 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Karreda: "Cohomology of infinitesimal quantum algebras"J.Algebra. 226. 818-856 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kashiwara: "Introduction to algebraic analysis"Iwanami (in Japanese). 250 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kashiwara: "Characters of irreducible modules with non-critical highest weights over affine Lie algebras."Proceedings of the International conference on representation theory. 275-296 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Kashiwara: "Parabolic Kazhdan-Lusztig polynomials and Schubert varieties"J.Algebra. (in press). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Kawanaka: "A q-Cauchy odentity for Schur functions and imprimtive complex reflection groups"Beitrage zur Algebra und Geometrie. 41. 115-140 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Shoji: "A Frobenius formula for the characters of Ariki-Koike algebras"Osaka J.Math.. (in press). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Shoji: "Length functions of G(r,p,n)"Advanced Studies in Pure Math.. 28. 327-342 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Kaneda: "Cohomology of inifinitesimal quantum algebras"J.Algebra. 226. 818-856 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 柏原正樹: "代数解析概論"岩波書店. 250 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Tanisaki: "Hypergeometric systems and Rcdon transforms for Hermition symmatric spaces"Advances in Mathematics. 26(in press). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Kashiwara: "Characters of irreducible modules with non-critical highest weights"Proceedings of the ICRT. (in press). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Iohara: "Hirota bilinear forms with 2-toraidel symmetry"Physics Letters A. 254. 37-46 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Takeuchi: "A Hartogs-type theoreun for solutions to systems with regelar singdarity"Arch. Math. (Basel). 73. 390-393 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Takeuchi: "Microlocal vanishing cycles and ramified Cauchy proddems in the Nilsson class"Compositio Math.. (in press). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Shoji: "A Frobenius formuda for the characters of Ariki-Koike algebras"J. Algebra. (in press). (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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