Weil Representations of Symplectic Groups Over Rings

Abstract

We are interested in Weil representations of Sp(2n, R), where R is the ring Z/plZ, p is an odd prime and l is a positive integer, or, more generally, R = O/pl, where O is the ring of integers of a local field, p is the maximal ideal of O and O/p has odd characteristic. One reason for this interest is that a continuous finite-dimensional complex representation of Sp(2n, O) has to factor through a representation of Sp(2n, O/pl) for some l.