February 20 - 22, 2014

Mini course

Representation theory of Lie algebra

of vector fields on a torus

will be given by

Professor Yuly Billig

 

School of Mathematics and Statistics

Carleton University, Ottawa

 Abstract

In this mini-course we will discuss the classification of simple weight modules for the Lie algebra of vector fields on a torus. We will begin with the elementary constructions of representations of a geometric nature - modules of tensor fields on a torus. We will discuss the question of irreducibility of these modules and the exceptional nature of the modules in the de Rham complex. The second family of irreducible modules that we introduce will be the class of bounded modules. We will present their vertex operator realizations and explain the construction of the chiral de Rham complex. Finally, we will discuss the proof of the classification theorem for the irreducible weight modules for the Lie algebra of vector fields on a torus.

Lecture notes of the mini course can be found here.

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Schedule

Thursday, February 20, 2014, 3 pm - 4:30 pm, room C-2033
Friday, February 21, 2014, 3 pm - 4:30 pm, room SN-2041
Saturday, February 22, 2014, 11 am - 12:30 pm, room HH-3017