Freeness of spherical Hecke modules of unramified U(2,1) in characteristic p

Abstract

Let F be a non-archimedean local field of odd residue characteristic p. Let G be the unramified unitary group U(2,1)(E/F) in three variables, and K be a maximal compact open subgroup of G. For an irreducible smooth representation σ of K over F‾p, we prove that the compactly induced representation indKGσ is free of infinite rank over the spherical Hecke algebra H(K,σ).