منابع مشابه
Partial orderings of an affine Weyl group
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 ...
متن کاملAffine Weyl Group Approach to Painlevé Equations
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 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...
متن کاملAffine Weyl group symmetry of the Garnier system
In this paper, we show that the Garnier system in n-variables has affine Weyl group symmetry of type B (1) n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(Cn+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.
متن کاملLEFT 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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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1987
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171287000188