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

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

2009-03-09

arxiv.org/abs/0903.1486v1

The Journal of Analysis, volume 17, pages 73-85, 2009

Mathematics

Representation Theory

Scientific paper

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.

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