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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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TBAbelian Ideals, KR--modules and Koszul algebras
Thursday March 13, 2008
02:00PM - 03:00PM
Speakers:
Vyjayanthi Chari
Abstract:
To each abelian ideal in a simple Lie algebra we associate a family of representation of the corresponding algebra of polynomial currents. In the case, when the abelian ideals satisfy some additional conditions, the representations are generalizations of the Kirillov--Reshetikhin modules. Moreover, under a suitable equivalence of categories, these modules correspond to right indecomposable projective modules of a finite--dimensional Koszul algebra.
Furthermore, we construct an infinite dimensional Koszul algebra associated to the abelian ideal with global dimension equal to the cardinality of the ideal. This is based on joint work with Jacob Greenstein.
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