Combinatorics of Schubert calculus and its application

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400041
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University 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
• 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

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.

Free Research Field

代数学