Star reducible Coxeter groups
| dc.creator | Green, R. M. | |
| dc.date | 2005-09-15 | |
| dc.date | 2006-08-24 | |
| dc.date.accessioned | 2026-07-07T06:43:02Z | |
| dc.date.available | 2026-07-07T06:43:02Z | |
| dc.description | We define ``star reducible'' Coxeter groups to be those Coxeter groups for which every fully commutative element (in the sense of Stembridge) is equivalent to a product of commuting generators by a sequence of length-decreasing star operations (in the sense of Lusztig). We show that the Kazhdan--Lusztig bases of these groups have a nice projection property to the Temperley--Lieb type quotient, and furthermore that the images of the basis elements $C'_w$ (for fully commutative $w$) in the quotient have structure constants in ${\Bbb Z}^{\geq 0}[v, v^{-1}]$. We also classify the star reducible Coxeter groups and show that they form nine infinite families (types $A_n$, $B_n$, $D_n$, $E_n$, $F_n$, $H_n$, affine $A_{n-1}$ for $n$ odd, affine $C_{n-1}$ for $n$ even, and the case where the Coxeter graph is complete), with two exceptional cases (of ranks 6 and 7). This paper is the sequel to math.QA/0509362. | |
| dc.description | Approximately 41 pages, AMSTeX, 4 figures. Revised in light of referee comments. To appear in the Glasgow Mathematical Journal | |
| dc.identifier | https://arxiv.org/abs/math/0509363 | |
| dc.identifier | http://arxiv.org/abs/math/0509363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102268 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 20F55, 20C08 | |
| dc.title | Star reducible Coxeter groups | |
| dc.type | text |