loop spaces and representations of real groups.'
(U. T. at Austin)
I will explain recent work with David
Nadler, in which we givea new description of representations of real
and complex Lie groups
in terms of coherent sheaves on complex algebraic varieties. Using the
language of derived algebraic geometry, which I'll survey, we
identify coherent sheaves on the space of unparametrized loops on an
algebraic variety with flat connections (D-modules) on the variety
itself.The main observation is then that some of the star playersin
representation theory, in particular the Steinberg variety and the
of Langlands parameters for Harish-Chandra modules, are naturally
identifiedas loop spaces. This provides a new bridge between the
Langlands program and geometric representation theory.
February 28th, Wednesday, 5:00-6:00 pm
will be served at 4:30pm