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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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Combinatorics of Coxeter elements and cluster algebras of finite type
Tuesday March 18, 2008
09:30AM - 10:30AM
Speakers:
Andrei Zelevinsky
Abstract:
In joint work with Shih-Wei Yang, we give a
unified geometric realization of the cluster algebra of an arbitrary finite
type with principal coefficients at any acyclic cluster (all necessary
notions from the theory of cluster algebras will be explained). Our
construction is based on the combinatorial study of orbits of
fundamental weights under the action of the cyclic group generated by
a Coxeter element. As an application, we obtain a much simplified
description of the Cambrian fans by N.Reading and D.Speyer.
Interestingly, very similar combinatorics appeared in a different
context in recent work by A.Kirillov, Jr. and J.Thind.
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