Mathematical Institute of the University of Bonn

Date and Time: 24 January 2025, 2:05pm

Location: MPIM Lecture Hall

Speaker: Michael Rapoport (Universität Bonn)

Title: A new basis of the spherical Hecke algebra and integral Hecke operators

Abstract: There are three well-known bases of the spherical Hecke algebra: the characteristic functions of double cosets, the inverse images under the Satake map of the monomial symmetric functions and the Kato-Lusztig basis. These are related by upper triangular base change matrices. In the talk, I will introduce two more bases, the nuclear basis and the atomic basis, again related by upper triangular base change matrices. I will explain how these new bases can be used to construct integral Hecke operators for automorphic vector bundles on some Shimura varieties. This is joint work with U. Goertz and X. He.