• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Representations of Hecke algebras

Research Project

Project/Area Number 14540014
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

ARIKI Susumu  KYOTO UNIVERSITY, Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (40212641)

Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
KeywordsHecke algebra / representation type
Research Abstract

The goal of this research is to study the modular representations of Hecke algebras of classical type, by using methods of Artin algebras. As the general theory of Artin algebras does not suffice to obtain concrete results for the Hecke algebras, the idea was to use my previous result, which allows us to compute the decomposition numbers of Hecke algebras of classical type (type B in particular), jointly with the general theory of Artin algebras.
After two years of research, we have obtained satisfactory results for the determination of representation types of the Hecke algebras. Main result is as follows.
Theorem. Let W be a Weyl group, Pw(x) be the Poincare polynomial of W, F an algebraically closed field, q ∈ F so that q ≠ 0,1. The associated Hecke algebra, which is an F-algebra, is denoted by Hw(q). Then, Hw(q) is finite, tame, wild if (x-q)^2 does not divide Pw(x), q = -1 ≠ 1 and (x + 1)^2 ‖ Pw(x) otherwise, respectively.
We also have the result for two parameter Hecke algebras in type B case.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] 有木 進: "古典型ヘッケ環の表現型について"数理解析研究所講究録. 1294. 1-7 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki: "On tameness of the Hecke algebras of type B"Contemp.Math.. 325. 11-30 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki: "Uno's conjecture on representation types of Hecke algebras"Algebraic Combinatorics and Quantum Groups. 1-9 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki, Andrew Mathas: "The representation type of Hecke algebras of type B"Adv.Math.. 181. 134-159 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki, Andrew Mathas: "Hecke algebras with a finite number of indecomposable modules."Representation Theory of Algebraic Groups and Quantum Groups. (校閲終了掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 有木 進: "古典型Hecke環のモジュラー表現"数学. 56(校閲終了掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki: "Representations of Quantum Algebras and Combinatorics of Young Tableaux"アメリカ数学会. 158 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki: "On representation types of Hecke algebras of classical type (Japanese)"RIMS kokyuroku. 1294. 1-7 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki: "On tameness of the Hecke algebras of type B"Contemp.Math.. 325. 11-30 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki: "Uno's conjecture on representation types of Hecke algebras"Algebraic Combinatorics and Quantum Groups World Scientific. 1-9 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki, A.Mathas: "The representation type of Hecke algebras of type B"Adv.Math.. 181. 134-159 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki, A.Mathas: "Hecke algebras with a finite number of indecomposable modules"Represeentation Theory of Algebraic Groups and Quantum Groups, Adv.Stud.Pure.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki: "Modular representations of Hecke algebras of classical type (Japanese)"Suugaku, Iwanami. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ariki: "Representations of Quantum Algebras and Combinatorics of Young Tableaux"Amer.Math.Soc.. 158 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Susumu Ariki: "On tameness of the Hecke algebras of type B"Contemp.Math.. 325. 11-30 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Susumu Ariki: "Lino's conjecture on representation types of Hecke algebras"Algebraic Combinatorics and Quantum Groups. 1-9 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Susumu Ariki, Andrew Mathas: "The representation type of Hecke algebras of type B"Adv.Math.. 181. 134-159 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 有木 進: "古典型Hecke環のモジュラー表現"数学. 56. 113-136 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Ariki: "Uno's conjecture on representation types of Hecke algebras"Contemp. Math.. (校閲終了掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Ariki: "On tameness of the Hecke algebras of type B"Contemp. Math.. (校閲終了掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Ariki (共著): "The representation type of Hecke algebras fo type B"Advances in Math.. (校閲終了掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Ariki (共著): "Hecke algebras with a finite number of indecomposable modules"Advances Studies in Pure Math.. (校閲終了掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] 有木 進: "古典型ヘッケ環の表現型について"数理解析研究所講究録. 1294. 1-7 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Ariki: "Representations of Quantum Algebras and Combinations of Young Tableaux"Amer. Math. Soc.. 158 (2002)

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi