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

Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravit