Resumen de Kazhdan¿Lusztig cells and the Murphy basis
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.
