Weil representations associated to finite quadratic modules
Abstract
To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z), on C[D], the group algebra of D. This representation is usually called the Weil representation associated to the finite quadratic module. The main result of this paper is a general explicit formula for the matrix coefficients of this representation. The formula, which involves the p-adic invariants of the quadratic module, is given in a way which is easy to implement on a computer. The result presented completes an earlier result by Scheithauer for the Weil representation associated to a discriminant form of even signature.
Cite
@article{arxiv.1108.0202,
title = {Weil representations associated to finite quadratic modules},
author = {Fredrik Strömberg},
journal= {arXiv preprint arXiv:1108.0202},
year = {2011}
}