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A noncommutative extension of the coincidence of dimensions

Research Project

Project/Area Number 22540003
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionMuroran Institute of Technology

Principal Investigator

MORITA Hideaki  室蘭工業大学, 工学研究科, 准教授 (90435412)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords(非可換)対称函数 / 対称群 / 次数表現 / (非可換)対称函数 / 非可換対称関数 / ホール=リトルウッド関数 / スプリンガー加群 / マクドナルド多項式 / 1のベキ根 / ハグルンドーハマン-レオア公式
Research Abstract

The Springer modules for the symmetric group have a certaincombinatorial property called the coincidence of dimensions. The reporter succeeded ingiving the property an interpretations in terms of representation theory of the symmetricgroup, based on the factorization formula for the Hall-Littlewood functions. In this study, Ihave intended to extend this theory in a noncommutative setting, and have succeeded ingiving a proper noncommutative extension of the Hall-Littlewood functions in my point ofview.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (13 results)

All 2013 2012 2010 Other

All Journal Article (7 results) (of which Peer Reviewed: 6 results) Presentation (4 results) Book (2 results)

  • [Journal Article] Anew determinant expression for theweighted Bartholdi zeta function of adigraph2013

    • Author(s)
      H. Mitsuhashi, H. Morita and I. Sato
    • Journal Title

      Electronic J. Combin

      Volume: 20(1)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A matrix-weighted zeta function of a graph2013

    • Author(s)
      H. Motsuhashi, H. Morita, I. Sato
    • Journal Title

      Linear and Multilinear Algebra

      Volume: ?

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new determinant expression for the weighted Bartholdi zeta function of a digraph2013

    • Author(s)
      H. Motsuhashi, H. Morita, I. Sato
    • Journal Title

      Electronic Journal of Combinatorics

      Volume: ?

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A bijective proof for the factorizationformula of Macdonald polynomials at rootsof unity2012

    • Author(s)
      F. Descouens, H. Morita and Y. Numata
    • Journal Title

      Euro. J. Combin

      Volume: 33 Pages: 1257-1264

    • URL

      http://www.sciencedirect.com/science/article/pii/S019566981200036

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a bijective proof of a factorization formula for Macdonald polynomial2012

    • Author(s)
      F. Descouens, H. Morita, Y. Numata,
    • Journal Title

      Europwan Journal of Combinatorics

      Volume: 33 Pages: 1257-1264

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a bijective proof of a factorization formula for Macdonald polynomials2012

    • Author(s)
      F.Descouens, H.Morita, Y.Numata
    • Journal Title

      European Journal of Combinatorics

      Volume: 33 Issue: 6 Pages: 1257-1264

    • DOI

      10.1016/j.ejc.2012.02.004

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Amatrix-weighted zeta function of a graph

    • Author(s)
      H. Mitsuhashi, H. Morita and I. Sato
    • Journal Title

      Linear and Multilinear Algebra

      Volume: (to appear)

    • URL

      http://www.tandfonline.com/doi/full/10.1080/03081087.2013.764496#.UbW2oBbTJjA

    • Related Report
      2012 Final Research Report
  • [Presentation] 非可換Hall-Littlewood 関数について組合せ論的表現論とその周辺2012

    • Author(s)
      三橋秀生-森田英章
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-10-12
    • Related Report
      2012 Final Research Report
  • [Presentation] マクドナルド多項式のベキ根における分解公式2010

    • Author(s)
      森田英章
    • Organizer
      BC 系とAGT 予想の周辺
    • Place of Presentation
      東京大学
    • Year and Date
      2010-09-12
    • Related Report
      2012 Final Research Report
  • [Presentation] マクドナルド多項式のベキ根における分解公式2010

    • Author(s)
      森田英章
    • Organizer
      BC系とAGT予想の周辺
    • Place of Presentation
      東京大学
    • Year and Date
      2010-09-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] 非可換 Hall-Littlewood 関数について

    • Author(s)
      三橋秀生ー森田英章
    • Organizer
      組合せ論的表現論とその周辺
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Book] The Lefschetz Properties2013

    • Author(s)
      T. Harima, T. Maeno, H. Morita, Y. Numata, A. Wachi, J. Watanabe
    • Publisher
      Springer
    • Related Report
      2012 Annual Research Report
  • [Book] Springer Lecture Note Series

    • Author(s)
      T. Harima, T. Maeno, H.Morita, Y. Numata, A. Wachi and J.Watanabe
    • Publisher
      The Lefschetz Properties
    • Related Report
      2012 Final Research Report

URL: 

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

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