NISHIYAMA Kyo    Department   Aoyama Gakuin University  Department of Mathematical Sciences, College of Science and Engineering    Position   Professor
Language	English
Publication Date	2024/02
Type	Academic Journal
Peer Review	Peer reviewed
Title	Action of Hecke algebra on the double flag variety of type AIII
Contribution Type	Collaboration
Journal	Advances in Applied Mathematics
Journal Type	Another Country
Publisher	Elsevier
Volume, Issue, Page	153
Total page number	19
International coauthorship	International coauthorship
Author and coauthor	Lucas Fresse, Kyo Nishiyama
Details	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.