Casselman's basis, Yang-Baxter basis, and Kostant-Kumar's twisted group algebra

Casselman's basis is the basis of Iwahori fixed vectors of a spherical representation of a connected reductive $p$-adic group over a non-archimedean local field, which is dual to the intertwining operators at the identity indexed by elements of the Weyl group. The problem of Casselman is to express Casselman's basis in terms of another natural basis, and vice versa. In this talk, using Yang-Baxter basis of Hecke algebra and Kostant-Kumar's twisted group algebra, we will show one solution to Casselman's problem. This is joint work with H. Naruse.Non UBCUnreviewedAuthor affiliation: SophiaFacult