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}
}
  • M. Geck
  • Published 11 April 2005
  • Mathematics
  • Proceedings of the London Mathematical Society
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. 
Se p 20 05 GENERALIZED JONES TRACES AND KAZHDAN – LUSZTIG BASES
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
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
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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
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Cellularity of the p-Canonical Basis for Symmetric Groups.
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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