Automata and 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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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 ...
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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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We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F (t1, . . . , tn) of WDVV equations of associativity polynomial in t1, . . . , tn−1, exp tn.
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2010
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-2010-00391-x