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Combinatorics of Schubert calculus and its application

Research Project

Project/Area Number 25400041
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Yamanashi (2015)
Okayama University (2013-2014)

Principal Investigator

NARUSE Hiroshi  山梨大学, 総合研究部, 教授 (20172596)

Co-Investigator(Renkei-kenkyūsha) IKEDA Takeshi  岡山理科大学, 理工学部, 教授 (40309539)
NAKAGAWA Masaki  岡山大学, 教育学研究科, 准教授 (50370036)
ISHIKAWA Masao  琉球大学, 教育学部, 教授 (40243373)
HAGIWARA Manabu  千葉大学, 理学研究科, 准教授 (80415728)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsシューベルト・カルキュラス / 同変コホモロジー / 同変K理論 / 対称函数 / グラスマン多様体 / 一般コホモロジー / シューア函数 / 退化跡 / Casselman問題 / Schur函数 / Hall-Littlewood函数 / 同変K-理論 / hook公式 / 組合せ論 / シューア関数
Outline of Final Research Achievements

We defined good polynomial representative of torus equivariant Schubert class in K-theory of flag varieties of the classical groups. We also give combinatorial formula for them. As an application of equivariant Schubert calculus we give a proof of the hook formula, which gives the number of standard tableaux on a given shape of partition. We also give a generalization of the hook formula and its equivariant K-theory version. By alanogy with this formula we get a solution to the Casselman's problem related to the representation of p-adic algebraic groups using some techinques of Schubert calculus.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (11 results)

All 2015 2014 2013 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (7 results) (of which Invited: 1 results) Remarks (3 results)

  • [Journal Article] Finite sum Cauchy identity for dual Grothendieck polynomials2014

    • Author(s)
      A. Lascoux and H. Naruse
    • Journal Title

      Proceedings of the Japan Academy, Series A, Mathematical Sciences

      Volume: 90 Issue: 7 Pages: 87-91

    • DOI

      10.3792/pjaa.90.87

    • NAID

      40020185467

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Casselman問題とDuality2015

    • Author(s)
      中筋 麻貴、成瀬 弘
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学(京都府京都市)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] K理論的Segre類について2015

    • Author(s)
      松村朝雄、池田岳、成瀬 弘、T.Hudson
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学(京都府京都市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
  • [Presentation] K理論的シューベルト類の行列式公式2015

    • Author(s)
      松村朝雄、池田岳、成瀬 弘、T.Hudson
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学(京都府京都市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
  • [Presentation] A Gysin formula for the universal Schur functions2015

    • Author(s)
      中川征樹、成瀬 弘
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Equivariant quantum cohomology of maximal isotropic Grassmannians2015

    • Author(s)
      成瀬 弘
    • Organizer
      東京海洋大学 国際研究会
    • Place of Presentation
      東京海洋大学
    • Year and Date
      2015-03-10 – 2015-03-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Schubert calculus and hook formula2014

    • Author(s)
      Hiroshi Naruse
    • Organizer
      Seminar Lotheringen de Combinatoire
    • Place of Presentation
      オーストリア(Strobl)
    • Year and Date
      2014-09-07 – 2014-09-10
    • Related Report
      2014 Research-status Report
  • [Presentation] Factorial Schur functions and vexillary permutations of types B,C and D2013

    • Author(s)
      成瀬 弘
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Remarks] 成瀬研究室

    • URL

      http://www.ccn.yamanashi.ac.jp/~hnaruse/index.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] Hiroshi NARUSE's Home Page

    • URL

      http://www.ccn.yamanashi.ac.jp/~hnaruse/index_e.htm

    • Related Report
      2014 Research-status Report
  • [Remarks] Homepage

    • URL

      http://ed-www.ed.okayama-u.ac.jp/~suugaku/naru/index_e.htm

    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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