Kazhdan¿Lusztig cells and the Murphy basis

• Autores: Meinolf Geck
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 3, 2006, págs. 635-665
• Idioma: inglés
• DOI: 10.1017/s0024611506015930
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• Resumen

  • 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.