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Graduate Algebra and Representation Theory Seminar

Another Proof of Modular Invariance

Alejandro Ginory - Rutgers University

Location:  Hill 701 (GSL)
Date & time: Wednesday, 17 April 2019 at 3:30PM - 4:30PM

Abstract: A very important result in the representation theory of affine Lie algebras is that the space spanned by the (properly normalized) characters of integrable highest weight modules is invariant under the action of certain congruence subgroups of SL(2,Z). Most proofs involve expressing the characters explicitly in terms of functions with modular invariance properties like theta functions, Eisenstein series, and Weierstrass P-functions. In this talk, we will discuss a method of proving modular invariance without resorting to expressing characters in terms of already known modular invariant function spaces. The proof will use a group presentation of the so-called double affine Weyl group.

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