On character values and decomposition of the Weil representation associated to a finite abelian group

Abstract

We develop a simple algebraic approach to the study of the Weil representation associated to a finite abelian group. As a result, we obtain a simple proof of a generalisation of a well-known formula for the absolute value of its character. We also obtain a new result about its decomposition into irreducible representations. As an example, the decomposition of the Weil representation of Sp_{2g}(Z/NZ) is described for odd N.

References in corpus (2)

• On Cuspidal Representations of General Linear Groups over Discrete Valuation Rings
• Inductive Algebras for Finite Heisenberg Groups

Cited by in corpus (4)

• Degenerations and orbits in finite abelian groups
• Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution
• On modular group representations associated to SO$(p{)}_2$-TQFTs
• Character correspondences above fully ramified sections and Schur indices