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arXiv:math/0610644 [math.RT]AbstractReferencesReviewsResources

The Character of the Weil Representation

Teruji Thomas

Published 2006-10-21, updated 2007-10-20Version 3

Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp(V). The final formulas are overtly free of choices (e.g. they do not involve the usual choice of a Lagrangian subspace of V). Along the way, in results similar to those of K. Maktouf, we relate the character to the Weil index of a certain quadratic form, which may be understood as a Maslov index. This relation also expresses the character as the pullback of a certain simple function from Mp(V\oplus V).

Comments: 19 pages, accepted to appear in the Journal of the LMS. This final arXiv version is pre-proof
Journal: J. LMS. (2) 77 (2008), 221-239
Categories: math.RT
Subjects: 11F27
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