๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Canonical left cells in affine Weyl groups

โœ Scribed by George Lusztig; Nanhua Xi


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
231 KB
Volume
72
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.

โœฆ Synopsis


If s E S is not special, it is still true that Q n Y, is non-empty; however, it may be a union of several left cells.

2. NOTATION AND RECOLLECTIONS

2.1. We refer to [l] for the definition of the basis (C,) of the Hecke algebra of ( W, S) and of the relation y< w on W. We shall write y -w instead of "y < w or w < y.


๐Ÿ“œ SIMILAR VOLUMES


On Generalized Cells in Affine Weyl Grou
โœ Kirsten Bremke ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 386 KB

We determine the lowest generalized two-sided cell for affine Weyl groups. We < < show that it consists of at most W generalized left cells, where W denotes the 0 0 corresponding finite Weyl group. For parameters coming from graph automorphisms, we prove that this bound is exact. For such parameters

Left Cells in the Affine Weyl Group of T
โœ Jian-yi Shi ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 434 KB

We find a representative set of left cells of the affine Weyl group W of type C a 4

Left Cells in the Weyl Group of Type E8
โœ Yu Chen ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 222 KB

The aim of the present paper is to give an explicit description for all the left cells of the Weyl group W of type E 8 . We first find a representative set for the left cells of W and then use it to describe these cells. Our results show that most of the left cells in W can be characterized by their

Random Walk in an Alcove of an Affine We
โœ David J. Grabiner ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 159 KB

We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this technique to walks in the alcoves of the classical affine Weyl groups. In all cases, we get determinant formulas for th