# Seminars & Colloquia Calendar

## Double Affine Weyl Groups, Congruence Subgroups, and Affine Kac-Moody Lie Algebras

#### Alejandro Ginory, Rutgers University

Location: ** Hill 525**

Date & time: Monday, 16 October 2017 at 12:00PM - 1:00PM

Abstract: The representation theory of important types of Lie algebras involve certain discrete groups called Weyl groups. Amongst these Lie algebras are the affine Kac-Moody Lie algebras which give rise to the so-called affine Weyl groups. A natural extension of these Weyl groups are the double affine Weyl groups. We will discuss how double affine Weyl groups admit a simple presentation, similar to those of Coxeter groups, that are naturally related to congruence subgroups of SL(2,Z) and characters of affine Kac-Moody Lie algebras (twisted and untwisted).

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