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KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS

Published online by Cambridge University Press:  13 October 2006

MEINOLF GECK
MEINOLF GECK
Affiliation:
Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 avenue Claude Bernard, F-69622 Villeurbanne Cedex, France Current address: Department of Mathematical Sciences, King's College, University of Aberdeen, Aberdeen, AB24 3UE, United [email protected]
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Abstract

Let $H$ be the Iwahori–Hecke algebra associated with $S_n$, the symmetric group on $n$ symbols. This algebra has two important bases: the Kazhdan–Lusztig basis and the Murphy basis. We establish a precise connection between the two bases, allowing us to give, for the first time, purely algebraic proofs for a number of fundamental properties of the Kazhdan–Lusztig basis and Lusztig's results on the $a$-function.

Keywords

20C08
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 3 , November 2006 , pp. 635 - 665
Copyright
2006 London Mathematical Society

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