Clifford theory of Weil representations of unitary groups

2018/05/04 by Shau, Moumita, Szechtman, Fernando
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.01857

Abstract

Let \mathcal O be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of \mathcal O by a nonzero power of its maximal ideal and let * be the involution that A inherits from \mathcal O. We consider various unitary groups \mathcal U_m(A) of rank m over A, depending on the nature of * and the equivalence type of the underlying hermitian or skew hermitian form. Each group \mathcal U_m(A) gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the Weil representation of \mathcal U_m(A) with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.

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