On Generalized Cells in Affine Weyl Groups
نویسندگان
چکیده
منابع مشابه
Left 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...
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We begin with a compact figure that can be folded into smaller replicas of itself, such as the interval or equilateral triangle. Such figures are in one-to-one correspondence with affine Weyl groups. For each such figure in n-dimensional Euclidean space, we construct a sequence of polynomials P/c: Rn —► Rn so that the mapping P^ is conjugate to stretching the figure by a factor A; and folding i...
متن کاملKazhdan-Lusztig cells in affine Weyl groups (with unequal parameters)
Acknowledgments First of all I wish to thank my supervisor Meinolf Geck who guided me through my Ph.D. studies. His patience, generosity and support made this thesis possible. I feel very fortunate to have been his student. My thoughts are going to Fokko du Cloux who was my supervisor in Lyon during the second year of my Ph.D. I would also like to thank Philippe Caldéro for being my supervisor ...
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Let W be a Weyl or affine Weyl group and let Wc be the set of fully commutative elements in W . We associate each w ∈ Wc to a digraph G(w). By using G(w), we give a graph-theoretic description for Lusztig’s a-function on Wc and describe explicitly all the distinguished involutions of W . The results verify two conjectures in our case: one was proposed by myself in [15, Conjecture 8.10] and the ...
متن کاملExcedances in classical and affine Weyl groups
Based on the notion of colored and absolute excedances introduced by Bagno and Garber we give an analogue of the derangement polynomials. We obtain some basic properties of these polynomials. Moreover, we define an excedance statistic for the affine Weyl groups of type B̃n, C̃n and D̃n and determine the generating functions of their distributions. This paper is inspired by one of Clark and Ehrenbo...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1997
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6889