Proceedings of the London Mathematical Society

Table of Contents - 2006 - Volume 93, Issue 03  


KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS

MEINOLF GECK a1p1
a1 Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 avenue Claude Bernard, F-69622 Villeurbanne Cedex, France

Article author query
geck m   [Google Scholar] 
 

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.

(Published Online October 13 2006)
(Received April 11 2005)

Maths Classification

20C08.

Correspondence:
p1 Current address: Department of Mathematical Sciences, King's College, University of Aberdeen, Aberdeen, AB24 3UE, United Kingdom m.geck@maths.abdn.ac.uk