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KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS

  • MEINOLF GECK (a1) (a2)

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.

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KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS

  • MEINOLF GECK (a1) (a2)

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