# Kazhdan–Lusztig Cells and the Murphy Basis

@article{Geck2005KazhdanLusztigCA, title={Kazhdan–Lusztig Cells and the Murphy Basis}, author={Meinolf Geck}, journal={Proceedings of the London Mathematical Society}, year={2005}, volume={93} }

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.

## 47 Citations

Se p 20 05 GENERALIZED JONES TRACES AND KAZHDAN – LUSZTIG BASES

- Mathematics
- 2005

We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the positivity of certain structure constants for the…

A pr 2 00 7 GENERALIZED JONES TRACES AND KAZHDAN – LUSZTIG BASES

- Mathematics
- 2007

We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the pos-itivity of certain structure constants for the…

Decomposition for Kazhdan–Lusztig basis elements of the affine Hecke algebra of type A˜n−1

- Mathematics
- 2017

RSK bases and Kazhdan-Lusztig cells

- Mathematics
- 2009

From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the…

Module structure of cells in unequal-parameter Hecke algebras

- MathematicsNagoya Mathematical Journal
- 2010

Abstract A conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in type Bn by families of standard domino tableaux of arbitrary…

Type $A$ admissible cells are Kazhdan–Lusztig

- Mathematics
- 2018

Admissible W-graphs were defined and combinatorially characterised by Stembridge in reference [12]. The theory of admissible W-graphs was motivated by the need to construct W-graphs for…

KRS bases for rings of invariants and for endomorphism spaces of irreducible modules

- Mathematics
- 2009

From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the…

Ordering Lusztig’s families in type Bn

- Mathematics
- 2012

Let W be a finite Coxeter group and L be a weight function on W in the sense of Lusztig. We have recently introduced a pre-order relation ⪯L on the set of irreducible characters of W which extends…

Cellularity of the p-Canonical Basis for Symmetric Groups.

- Mathematics
- 2020

For symmetric groups we show that the p-canonical basis can be extended to a cell datum for the Iwahori-Hecke algebra H and that the two-sided p-cell preorder coincides with the Kazhdan-Lusztig…

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