منابع مشابه
The Second Lowest Two-sided Cell in an Affine Weyl Group
Let Wa be an irreducible affine Weyl group with W0 the associated Weyl group. The present paper is to study the second lowest two-sided cell Ωqr of Wa. Let nqr be the number of left cells of Wa in Ωqr. We conjecture that the equality nqr = 1 2 |W0| should always hold. When Wa is either e An−1, n > 2, or of rank 6 4, this equality can be verified by the existing data (see 0.3). Then the main res...
متن کاملOn the Lowest Two-sided Cell in Affine Weyl Groups
Bremke and Xi determined the lowest two-sided cell for affineWeyl groups with unequal parameters and showed that it consists of at most |W0| left cells where W0 is the associated finite Weyl group. We prove that this bound is exact. Previously, this was known in the equal parameter case and when the parameters were coming from a graph automorphism. Our argument uniformly works for any choice of...
متن کاملPartial 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 Partial Order on Two-sided Cells of Certain Affine Weyl Groups
In their famous paper [6], Kazhdan and Lusztig introduced the concept of equivalence classes such as left cell, right cell and two-sided cell in a Coxeter group W . We inherit the notations 6 L , 6 R , 6 LR , ∼ L , ∼ R and ∼ LR in [6]. Thus w ∼ LR y (resp. w ∼ L y, resp. w ∼ R y) means that the elements w, y ∈ W are in the same two-sided cell (resp. left cell, resp. right cell) of W , etc. Conc...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1987
ISSN: 0024-6107
DOI: 10.1112/jlms/s2-36.3.407