%0 Journal Article %1 geck2006kazhdanlusztig %A Geck, Meinolf %D 2006 %I Cambridge University Press %J Proceedings of the London Mathematical Society %K from:meinolfgeck from:geck %N 3 %P 635-665-- %R DOI: 10.1017/S0024611506015930 %T Kazhdan-Lusztig cells and the Murphy basis %U https://www.cambridge.org/core/article/kazhdanlusztig-cells-and-the-murphy-basis/C239D2F91F7317252AE3E5CA041F4C61 %V 93 %X 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.

@article{geck2006kazhdanlusztig, 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.}, added-at = {2021-07-11T11:06:08.000+0200}, author = {Geck, Meinolf}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/242271731d679323a5ec406a3ca9b7a96/mathematik}, doi = {DOI: 10.1017/S0024611506015930}, interhash = {d25875ed4a93d58fa4f3defd8e890aeb}, intrahash = {42271731d679323a5ec406a3ca9b7a96}, issn = {00246115}, journal = {Proceedings of the London Mathematical Society}, keywords = {from:meinolfgeck from:geck}, number = 3, pages = {635-665--}, publisher = {Cambridge University Press}, timestamp = {2021-07-11T09:06:08.000+0200}, title = {Kazhdan-Lusztig cells and the Murphy basis}, url = {https://www.cambridge.org/core/article/kazhdanlusztig-cells-and-the-murphy-basis/C239D2F91F7317252AE3E5CA041F4C61}, volume = 93, year = 2006 }