## W-graph ideals and biideals

### Robert B. Howlett and Van Minh Nguyen

#### Abstract

We further develop the theory of $$W\!$$-graph ideals, first introduced by the authors in reference [6]. We discuss $$W\!$$-graph subideals, and induction and restriction of $$W\!$$-graph ideals for parabolic subgroups. We introduce $$W\!$$-graph biideals: those $$W\!$$-graph ideals that yield $$(W\times W^{\mathrm o})$$-graphs, where $$W^{\mathrm o}$$ is the group opposite to $$W$$. We determine all $$W\!$$-graph ideals and biideals in finite Coxeter groups of rank 2.

Keywords: Coxeter groups, Hecke algebras, W-graphs, Kazhdan–Lusztig polynomials, cells.

: Primary 20C08.

This paper is available as a pdf (364kB) file.

 Tuesday, March 3, 2015