On the Hecke algebra of a type for unramified \(p\)-adic unitary groups
Let \(F\) be a non-Archimedean local field with odd residue characteristic that is equipped with a Galois involution with fixed field \(F_o\). Let \(G\) be either the symplectic group \(Sp_{2N}(F)\) over \(F\) or an unramified unitary group over \(F_o\). The key result of this paper is the following Theorem: If a pair (\(J_P, \lambda_P)\) in the unramified group \(G\) that consists of a Levi subgroup \(M\) of \(G\) and of an irreducible supercuspidal representation \(\pi\) of \(M\) is of simple type, then the Hecke algebra \(H(G, \lambda_P)\) is generic.
irreducible supercuspidal representation
scientific article; zbMATH DE number 5718174
scientific article