ニシヤマ　キョウ   NISHIYAMA Kyo   西山　享    所属   青山学院大学  理工学部 数理サイエンス学科    職種   教授
言語種別	英語
発行・発表の年月	2024/02
形態種別	学術雑誌
査読	査読あり
標題	Action of Hecke algebra on the double flag variety of type AIII
執筆形態	共同
掲載誌名	Advances in Applied Mathematics
掲載区分	国外
出版社・発行元	Elsevier
巻・号・頁	153
総ページ数	19
国際共著	国際共著
著者・共著者	Lucas Fresse, Kyo Nishiyama
概要	Abstract: Consider a connected reductive algebraic group G and a symmetric subgroup K. Let X=K/BK×G/P be a double flag variety of finite type, where BK is a Borel subgroup of K, and P a parabolic subgroup of G. A general argument shows that the orbit space CX/K inherits a natural action of the Hecke algebra H=H(K,BK) of double cosets via convolutions. However, it is a quite different problem to find out the explicit structure of the Hecke module. In this paper, for the double flag variety of type AIII, we determine the explicit action of H on CX/K in a combinatorial way using graphs. As a by-product, we also get the description of the representation of the Weyl group on CX/K as a direct sum of induced representations.