The Character of the Weil Representation

Details The Character of the Weil Representation The Character of the Weil Representation

2006-10-21

arxiv.org/abs/math/0610644v3

Mathematics

Representation Theory

19 pages, accepted to appear in the Journal of the LMS. This final arXiv version is pre-proof

Scientific paper

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).

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