Admissible -graphs

Author:
John R. Stembridge

Journal:
Represent. Theory **12** (2008), 346-368

MSC (2000):
Primary 20F55, 20C15; Secondary 05E99

Published electronically:
October 9, 2008

MathSciNet review:
2448288

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a Coxeter group , a -graph encodes a module for the associated Iwahori-Hecke algebra . The strongly connected components of , known as cells, are also -graphs, and their modules occur as subquotients in a filtration of . Of special interest are the -graphs and cells arising from the Kazhdan-Lusztig basis for the regular representation of . We define a -graph to be admissible if, like the Kazhdan-Lusztig -graphs, it is edge-symmetric, bipartite, and has nonnegative integer edge weights. Empirical evidence suggests that for finite , there are only finitely many admissible -cells. We provide a combinatorial characterization of admissible -graphs, and use it to classify the admissible -cells for various finite of low rank. In the rank two case, the nontrivial admissible cells turn out to be -- Dynkin diagrams.

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Additional Information

**John R. Stembridge**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043

Email:
jrs@umich.edu

DOI:
http://dx.doi.org/10.1090/S1088-4165-08-00336-1

Received by editor(s):
June 8, 2008

Published electronically:
October 9, 2008

Additional Notes:
This work was supported by NSF Grant DMS–0554278.

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.