✦ LIBER ✦
T-Increasing Paths on the Bruhat Graph of Affine Weyl Groups are Self-Avoiding
✍ Scribed by Paola Cellini
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 119 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let W, S be a Coxeter system, T s wsw ¬ s g S, w g W its set of reflections, $ any total reflection order, and ⌫ the undirected Bruhat graph. We Ä 4 consider the natural labeling of the edges of ⌫ which assigns to the edge ¨, w the reflection ¨wy1 . A path on ⌫, i.e., a sequence ¨, . . . , ¨such that ¨¨y1 g T for
paths play an important role in the computation of both the Kazhdan᎐Lusztig and the R-polynomials of W. We prove that if W is finite or is an affine Weyl group, then any T-increasing path is self-avoiding, i.e., it has no self-intersection points.