منابع مشابه
LEFT CELLS IN THE AFFINE WEYL GROUP Wa(D̃4)
The cells of affine Weyl groups have been studied for more than one decade. They have been described explicitly in cases of type Ãn ( n ≥ 1 ) [13][9] and of rank ≤ 3 [1][4][10]. But there are only some partial results for an arbitrary irreducible affine Weyl group [2][7][8][16][17]. In [18], we constructed an algorithm to find a representative set of left cells of certain crystallographic group...
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In this note we draw together some of the scattered literature dealing with several partial orderings of affine Weyl groups. Most of the theory was developed as a tool in the study of modular representations for groups of Lie type, but here we focus just on an affine Weyl group Wa in its elementary geometric setting while sometimes invoking also its structure as a Coxeter group. While notation ...
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An overview is given on recent developments in the affine Weyl group approach to Painlevé equations and discrete Painlevé equations, based on the joint work with Y. Yamada and K. Kajiwara. 2000 Mathematics Subject Classification: 34M55, 39A12, 37K35.
متن کاملLeft Cells in Affine Weyl Groups
We prove a property of left cells in certain crystallographic groups W , by which we formulate an algorithm to find a representative set of left cells of W in any given two-sided cell. As an illustration, we make some applications of this algorithm to the case where W is the affine Weyl group of type e F4. The cells of affine Weyl groups W , as defined by Kazhdan and Lusztig in [6], have been d...
متن کاملThe module of affine descent classes of a Weyl group
The goal of this paper is to introduce an algebraic structure on the space spanned by affine descent classes of a Weyl group, by analogy and in relation to the structure carried by ordinary descent classes. The latter classes span a subalgebra of the group algebra, Solomon’s descent algebra. We show that the former span a left module over this algebra. The structure is obtained from geometric c...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90030-r