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The Weil Character of the Unitary Group Associated to a Finite Local Ring

Published online by Cambridge University Press:  20 November 2018

Roderick Gow  and
Fernando Szechtman
Roderick Gow
Affiliation:
Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland, email: rod.gow@ucd.ie
Fernando Szechtman*
Affiliation:
Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland, email: rod.gow@ucd.ie
*
Current address: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, email: fszechtm@herod.uwaterloo.ca
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Abstract

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Let $\mathbf{R}/R$ be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote by ${{\mathbf{U}}_{n}}\left( \mathbf{R} \right)$ the unitary group of rank $n$ associated to $\mathbf{R}/R$. The Weil representation of ${{\mathbf{U}}_{n}}\left( \mathbf{R} \right)$ is defined and its character is explicitly computed.

Keywords

20G05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 6 , 01 December 2002 , pp. 1229 - 1253
Copyright
Copyright © Canadian Mathematical Society 2002

References

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