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(Sigma), rho (Sigma)) of an open compact subgroup J(Sigma) and its irreducible representation rho (Sigma) which is constructed from given data Sigma = (Gamma, P'(0), rho). Here, Gamma is a semisimple element in the Lie algebra of G, P'(0) is a parahoric subgroup in the centralizer of Gamma in G, and rho is a cuspidal representation on the finite reductive quotient of P'(0). In this paper, we explicitly describe those Hecke algebras when P'(0) is a minimal parahoric subgroup, rho is trivial and rho (Sigma) is a character. [References: 18]
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