Kazhdan–Lusztig Cells and the Murphy Basis

By Meinolf Geck. 2005

63 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7c66de46db0b26d0692f557eb12ab444e41023f

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In Discrete Mathematics and Combinatorics

1. Meinolf Geck
2. Nicolas Jacon

In Geometry and Topology

1. Meinolf Geck
2. Nicolas Jacon

In Mathematical Physics

1. Meinolf Geck
2. Nicolas Jacon

Citations in the corpus

• Hecke algebras of finite type are cellular (2006, background): “The exact relation between the two cellular structures is determined in [9].”