Coxeter Elements and Kazhdan–Lusztig Cells

✍ Scribed by Jian-yi Shi

• Book ID: 102575847
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 212 KB
• Volume: 250
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9090

✦ Synopsis

By the correspondence between Coxeter elements of a Coxeter system W S and the acyclic orientations of the Coxeter graph , we study some properties of elements in the set C 0 W . We show that when W is of finite, affine, or hyperbolic type, any w ∈ C 0 W satisfies w ∼ LR w J with w J = J = m w for some J ⊂ S. Now assume that W is of finite or affine type. We give an explicit description for all the distinguished involutions d of W with d ∼ L w for some w ∈ E W , which verifies a conjecture proposed in [Jian-yi Shi, Adv. Sci. China, Math. 3 (1990), 79-98, Conjecture 8.10] in our case. We show that any left cell of W containing some element of C 0 W is left-connected, which verifies a conjecture of Lusztig [Ryoshi Hotta (Ed.), in "Problems from the Conference on Algebraic Groups and Representations held at Katata, August 29-September 3, 1983"] in our case.  2002 Elsevier Science (USA)