Admissible W-graphs
Monday March 17, 2008
09:15AM - 10:30AM
Speakers:
John Stembridge
Abstract:
Given a Coxeter group W, a W-graph is a combinatorial structure
that encodes a representation of W, or more generally, a module
for the associated Iwahori-Hecke algebra. By a theorem of Gyoja,
it is known that every irreducible representation of a finite
Coxeter group may be realized as a W-graph. Of special interest
are the W-graphs that encode the Kazhdan-Lusztig cell
representations of Hecke algebras, and more generally, the cell
representations associated to blocks of irreducible representations
of real Lie groups.
In this talk, we will discuss a class of "admissible" W-graphs
that have a very minimal set of defining properties; these
properties are designed so as to include all of the cells that
occur in Kazhdan-Lusztig theory. Remarkably, the admissible
W-graphs can be characterized by a simple set of combinatorial
rules, and yet there seem to be very few admissible W-cells other
than Kazhdan-Lusztig cells. In particular, all results obtained
so far support the hypothesis that there are only finitely many
admissible W-cells for each finite W.
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