Hecke Algebras of Classical Groups over p-adic Fields II

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G defined over p-adic fields in order to understand their admissible representations. Each Hecke algebra is associated to a pair (J, ) of an open compact subgroup J and its irreducible representation which is constructed from given data = (, P₀, ). Here, is a semisimple element in the Lie algebra of G, P₀ is a parahoric subgroup in the centralizer of in G, and is a cuspidal representation on the finite reductive quotient of P₀. In this paper, we explicitly describe those Hecke algebras when P₀ is a minimal parahoric subgroup, is trivial and is a character.