Cocenter of p-adic groups, II: Induction map

Abstract

In this paper, we study some relation between the cocenter H¯(G) of the Hecke algebra H(G) of a connected reductive group G over a nonarchimedean local field and the cocenter H¯(M) of its Levi subgroups M. Given any Newton component of H¯(G), we construct the induction map i¯ from the corresponding Newton component of H¯(M) to it. We show that this map is an isomorphism. This leads to the Bernstein–Lusztig type presentation of the cocenter H¯(G), which generalizes the work [11] on the affine Hecke algebras. We also show that the map i¯ we constructed is adjoint to the Jacquet functor.