1,007,503 research outputs found
The Character of the Weil Representation
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).Comment: 19 pages, accepted to appear in the Journal of the LMS. This final
arXiv version is pre-proo
Representation and character theory in 2-categories
We define the character of a group representation in a 2-category C. For
linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory
defined on pairs of commuting elements of the group. We discuss some examples
and prove a formula for the character of the induced representation.Comment: 34 pages, revised version, to appear in Advances in Mathematic
An explicit conductor formula for
We prove an explicit formula for the conductor of an irreducible, admissible
representation of twisted by a character of where
the field is local and non-archimedean. As a consequence, we quantify the
number of character twists of such a representation of fixed conductor
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