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Generating weights for modules of vector-valued modular forms

Banff International Research Station for Mathematical Innovation and Discovery

Vector-valued modular forms have recently been studied for applications to conformal field theory. In this talk, given an n-dimensional representation of the metaplectic group (e.g. the Weil representation of a finite quadratic module) we study the module of vector-valued modular forms for this representation, using methods from algebraic geometry. We prove that this module is free of rank n over the ring of level one modular forms, and we discuss the problem of finding the weights of a generating set. For Weil representations of cyclic quadratic modules of order 2p, p a prime, we show how the generating weights can be expressed in terms of class numbers of quadratic imaginary fields, and compute the distribution of the weights as p goes to infinity. This is joint work with Cameron Franc (U. Sask.) and Gene Kopp (U. Michigan).

Mathematics; Number theory; Algebraic geometry

video/mp4

Author affiliation: Louisiana State University

2017-03-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61015

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/