M.Nakasuji, A new approach in Schubert calculus to Casselman's problem,

Casselman basis is the basis of the vectors in a spherical representation of a reductive p-adic group that are fixed by the Iwahori subgroup. Casselman’s problem is to express it in terms of the natural basis of Iwahori-fixed vectors.

In this talk, we will discuss this problem from the view point of Schubert calculus. This will be a report on a joint work in progress with H.Naruse. More precisely, we will see our new approach compared with that by Brubaker-Bump-Licata using the Demazure-Lusztig operators.