A Weighted Enumeration of Maximal Chains in the Bruhat Order |
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Authors: | John R. Stembridge |
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Affiliation: | (1) Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109, USA |
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Abstract: | Given a finite Weyl group W with root system , assign the weight to each covering pair in the Bruhat order related by the reflection corresponding to . Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat ordering of any parabolic quotient of W. Several variations and open problems are discussed. |
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Keywords: | Bruhat order Weyl group root system |
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