Kazhdan--Lusztig cells and the Murphy basis
| dc.creator | Geck, Meinolf | |
| dc.date | 2005-04-11 | |
| dc.date | 2005-04-27 | |
| dc.date.accessioned | 2026-07-07T05:18:59Z | |
| dc.date.available | 2026-07-07T05:18:59Z | |
| dc.description | 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. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction of the representations of $H$, including the Dipper--James theory of Specht modules. In this paper, 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. | |
| dc.description | 34 pages; the revised version corrects some minor errors | |
| dc.identifier | https://arxiv.org/abs/math/0504217 | |
| dc.identifier | http://arxiv.org/abs/math/0504217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74856 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C08 | |
| dc.title | Kazhdan--Lusztig cells and the Murphy basis | |
| dc.type | text |