A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods 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 regular cases in general. We will give several examples of classical groups where the Schur multipliers are actually trivial.
Almost cyclic elements in Weil representations of finite classical groups
Characterizing finite $p$-groups by their Schur multipliers
Algebraic Groups over Finite Fields: Connections Between Subgroups and Isogenies
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