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Journal of the London Mathematical Society Advance Access originally published online on December 17, 2007
Journal of the London Mathematical Society 2008 77(1):221-239; doi:10.1112/jlms/jdm098
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© 2007 London Mathematical Society

The character of the Weil representation

Teruji Thomas

Merton College, Oxford, OX1 4JD, United Kingdom

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 (for example, they do not involve the usual choice of a Lagrangian subspace of V). Along the way, in results similar to those of 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).

2000 Mathematics Subject Classification 11F27.

This work was partially supported by NSF grants DMS-9977134 and DMS-0401164 and by the University of Chicago.

Received January 19, 2007; revised July 3, 2007; published online December 17, 2007.


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