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.

Wednesday, May. 06, 4:30 – 5:30 p.m.
Mathematics 520
Tea will be served at 4:00 p.m.

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