On the Hecke algebra of a type for unramified p-adic unitary groups

Let F be a non-archimedean local field of odd residue characteristic equipped with a galois involution with fixed field F0, and let G be a symplectic group over F or an unramified unitary group over F0. For a simple type (JP,λP) in G, which is a G-cover, associated to a certain simple stratum, we show that the corresponding Hecke algebra H(G,λP) is generic.