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Lie Theory |
| March 10, 2008 to March 14, 2008 |
| Organized By: Alexander Kleshchev, Arun Ram, Richard Stanley (chair), Bhama Srinivasan |
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| Parent Programs: |
| Combinatorial Representation Theory |
| Representation Theory of Finite Groups and Related Topics |
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| Return to Workshop Description |
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Sheaves on affine flag varieties, modular representations and Lusztig's conjecture
Tuesday March 11, 2008
03:30PM - 04:30PM
Speakers:
Peter Fiebig
Abstract:
Let $k$ be a field of positive characteristic. We
relate sheaves of $k$-vector spaces on a complex affine
flag variety to representations of the Lie algebra
associated to Langlands dual root system. From this we
extract a new proof of Lusztig's multiplicity conjecture
for
almost all characteristics. The main step in the
construction of the above relation is a categorification of
a natural map from the affine Hecke algebra to its periodic
module via the theory of sheaves on moment graphs. Using
this categorification we can also give a
non-topological proof of the multiplicity one case of
Lusztig's conjecture for all characteristics above the
Coxeter number.
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