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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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Sortable elements -- beyond finite type
Tuesday March 18, 2008
04:00PM - 05:00PM
Speakers:
David Speyer
Abstract:
In a finite Coxeter group $W$, Nathan Reading introduced "sortable elements" in
order to relate two of the objects enumerated by $W$-Catalan numbers: the variables in the
$W$-cluster algebra and the noncrossing partitions for $W$. Research started by Nathan
Reading, and completed by he and I, gives very precise and simple connections between sortable
elements, cluster algebras, non-crossing partitions and semi-invariants of quiver
representations. More recently, we have found analogues of our results that hold for all
Coxeter groups, not only the finite ones. I will explain this work, and describe some of the
intriguing new phenomena which appear when we leave the finite case. Although this work
relates to a number of mathematical fields -- quiver representations, Coxeter groups and
cluster algebras -- I will try to provide enough sketches so that listeners unfamiliar with
these fields can still follow the talk.
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