Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata

被引：2

作者：

Belolipetsky, Mikhail V. ^{[1
]}

Gunnells, Paul E. ^{[2
]}

Scott, Richard A. ^{[3
]}

机构：

[1] IMPA, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Massachusetts, Amherst, MA 01003 USA

[3] Santa Clara Univ, Santa Clara, CA 95053 USA

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2014年 / 24卷 / 05期

关键词：

Kazhdan-Lusztig cells; hyperbolic groups; finite state automata; REPRESENTATIONS;

D O I：

10.1142/S0218196714500325

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let C be a one- or two-sided Kazhdan-Lusztig cell in a Coxeter group (W, S), and let Red(C) be the set of reduced expressions of all w is an element of C, regarded as a language over the alphabet S. Casselman has conjectured that Red(C) is regular. In this paper, we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Casselman's.

引用

页码：757 / 772

页数：16