Lusztig's $a$-function in type $B_n$ in the asymptotic case
| dc.creator | Geck, Meinolf | |
| dc.creator | Iancu, Lacrimioara | |
| dc.date | 2005-04-11 | |
| dc.date | 2005-09-05 | |
| dc.date.accessioned | 2026-07-07T05:18:58Z | |
| dc.date.available | 2026-07-07T05:18:58Z | |
| dc.description | In this paper, we study Lusztig's $a$-function for a Coxeter group with unequal parameters. We determine that function explicitly in the ``asymptotic case'' in type $B_n$, where the left cells have been determined in terms of a generalized Robinson--Schensted correspondence by Bonnafé and the second author. As a consequence, we can also show that all of Lusztig's conjectural properties (P1)--(P15) hold in this case, except possibly (P9), (P10) and (P15). Our methods rely on the ``leading matrix coefficients'' introduced by the first author. We also interprete the ideal structure defined by the two-sided cells in the associated Iwahori--Hecke algebra $\bH_n$ in terms of the Dipper--james--Murphy basis of $\bH_n$. | |
| dc.description | 34 pages; revised, final version, to appear in Nagoya Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0504213 | |
| dc.identifier | http://arxiv.org/abs/math/0504213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74853 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C08 | |
| dc.title | Lusztig's $a$-function in type $B_n$ in the asymptotic case | |
| dc.type | text |