Langlands correspondence for loop groups
Lie Theory
March 13, 2008 11:00 AM to 12:00 PM
Speakers:
Frenkel, Edward
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Abstract: |
For a complex reductive group G, the local geometric Langlands
correspondence assigns to a local system on the punctured disc for the
Langlands dual group of G, a category equipped with an action of the
formal loop group G((t)). I will discuss a conjectural description of
these categories, due to Gaitsgory and myself, as categories of
representations of the corresponding affine Kac-Moody algebra of critical
level. Sometimes these categories may also be realized as categories of
D-modules or O-modules on some algebraic varieties or ind-schemes.
Interrelations between these categories provide supporting evidence for
our conjectures. In particular, we prove that the categories of Iwahori
equivariant representations of critical level with fixed central character
are equivalent to the categories of quasicoherent sheaves on the Springer
fibers the Langlands dual group. |
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Lecture #12682
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