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Topics in Combinatorial Representation Theory |
| March 17, 2008 to March 21, 2008 |
| Organized By: Sergey Fomin, Bernard Leclerc, Vic Reiner (Chair), Monica Vazirani |
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| Parent Programs: |
| Combinatorial Representation Theory |
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| Return to Workshop Description |
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Dual semicanonical bases and cluster algebras
Tuesday March 18, 2008
11:00AM - 12:00PM
Speakers:
Jan Schroeer
Abstract:
This is a report on joint work with Christof Geiss and
Bernard Leclerc.
Lusztig constructed a semicanonical basis of the universal
enveloping algebra of the positive part of a symmetric
Kac-Moody Lie algebra.
Using the representation theory of preprojective algebras
we want to study and construct multiplicative subsets
of the dual of the semicanonical basis.
(A set of dual basis vectors $b_1,\ldots,b_r$ is called multiplicative
if any monomial in these vectors belongs again to the dual basis.)
This yields a connection to Fomin and Zelevinsky's theory
of cluster algebras.
For simplicity we restrict to the case ${\rm sl}_n$.
But at the end of the talk, we will try to explain how
to generalize our results from ${\rm sl}_n$ to
arbitrary symmetric Kac-Moody algebras.
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