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Department Colloquium
May 6, 2015 @ 4:30 pm - 5:30 pm
Speaker: Constantin Teleman (UC Berkeley)
Title: Geometric Dequantization
Abstract: The well-known orbit method of Kirillov and Kostant produces unitary representations of Lie groups by the geometric quantization construction applied to orbits in the dual of the Lie algebra. The “trace’’ of this construction gives the orbital integral version of character formulae. A converse Dirac family construction extracts the geometric quantization data (orbit, line bundle and connection) from each representation. Freed, Hopkins and the speaker had used this to describe the K-group of the category of representations of loop groups of compact Lie groups in topological terms; but a re-intepretation using the notion of matrix factorizations nails the category of representations. Generalization to real semi-simple Lie groups suggests a classification of tempered representations of the loop groups of the respective loop groups.