Affine descents and the Steinberg torus

2007/09/27 by Kevin Dilks, Dilks, Kevin, T. Kyle Petersen +3 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Mathematics and Applications #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.0709.4291

Abstract

Let W\ltimes 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.

Citations

• Some Permutation Representations of Weyl Groups Associated with the Cohomology of Toric Varieties

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