Kevin Dilks ; T. Kyle Petersen ; John R. Stembridge
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Affine descents and the Steinberg torus
dmtcs:3631 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
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https://doi.org/10.46298/dmtcs.3631
Affine descents and the Steinberg torusConference paper
Authors: Kevin Dilks 1; T. Kyle Petersen 1; John R. Stembridge 1
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Kevin Dilks;T. Kyle Petersen;John R. Stembridge
1 Department of Mathematics - University of Michigan
Let W⋉L be an irreducible affine Weyl group with Coxeter complex Σ, where W denotes the associated finite Weyl group and L the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of Σ by the lattice L. We show that the ordinary and flag h-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over W for a descent-like statistic first studied by Cellini. We also show that the ordinary h-polynomial has a nonnegative γ-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the h-polynomials of Steinberg tori.
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