Proc. London Math. Soc.
Abstract of Paper PLMS 1593
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.
2000 Mathematics Subject Classification: 20C08.
E-mail:
m.geck@maths.abdn.ac.uk
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