Affiliation:
1. Department of Mathematics and Statistics , University of Regina , Regina , S4S 0A2 , Canada
Abstract
Abstract
Let
𝒪
{\mathcal{O}}
be an involutive discrete valuation ring with residue field of characteristic not 2.
Let A be a quotient of
𝒪
{\mathcal{O}}
by a nonzero power of its maximal ideal, and let
*
{*}
be the involution that A inherits from
𝒪
{\mathcal{O}}
.
We consider various unitary groups
𝒰
m
(
A
)
{\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
𝒰
m
(
A
)
{\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
𝒰
m
(
A
)
{\mathcal{U}_{m}(A)}
with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.
Subject
Algebra and Number Theory
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