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Proceedings of the London Mathematical Society 2006 93(3):635-665; doi:10.1017/S0024611506015930
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© London Mathematical Society

Kazhdan–Lusztig Cells and the Murphy Basis

Meinolf Geck

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

Received 11 April 2005.

Let H be the Iwahori–Hecke algebra associated with Sn, 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.

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


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