Title: Regular irreducible characters of a hyperspecial compact group,
Abstract: A parametrization of irreducible unitary representations associated with the
regular adjoint orbits of a hyperspecial compact subgroup of a reductive group
over a non-dyadic non-archimedean local filed is presented. The parametrization
is given by means of (a subset of) the character group of certain finite
abelian groups arising from the reductive group. Our method is based upon
Cliffod's theory and Weil representations over finite fields. It works under an
assumption of the triviality of certain Schur multipliers defined for an
algebraic group over a finite field. The assumption of the triviality has good
evidences in the case of general linear groups and highly probable in general.