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Thursday, September 11, 2014 -
11:35 to 12:35
Dr. Tanusree Khandai
Integrable representations of Multiloop Lie algebras of type $A_1$
Abstract: Given a finite-dimensional simple Lie algebra L, one can define a Lie algebra structure on $M = L \otimes \mathbb{C}[t_1^{\pm1},...t_n^{\pm1}]$, $ n\in \mathbb{Z}_+$. Such a Lie algebra is called a multiloop Lie algebra. The aim of the talk is to present a class of integrable representations for the multiloop Lie algebra $sl(2,\mathbb{C}) \otimes \mathbb{C}[t_1^{\pm1},...t_n^{\pm1}]$ . In order to do so, I shall begin with basic definitions and results of finite dimensional Lie algebras. Then discuss in detail the irreducible $sl(2,\mathbb{C})$-modules which play an important role in the representation theory of the multiloop Lie algebras.

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