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A parametrization of irreducible representations associated with a regularadjoint orbit of a classical group over finite quotient rings of the ring ofinteger of a non-dyadic non-archimedean local field is presented. Theparametrization is given by means of (a subset of) the character group of thecentralizer of a representative of the regular adjoint orbit. Our method isbased upon Weil representations over finite fields. More explicitparametrization in terms of tamely ramified extensions of the base field isgiven for the general linear group, the special linear group, the symplecticgroup and the orthogonal group.

Regular irreducible represntations of classical groups over finite quotient rings