Affine descents and the Steinberg torus
| dc.creator | Dilks, Kevin | |
| dc.creator | Petersen, T. Kyle | |
| dc.creator | Stembridge, John | |
| dc.date | 2007-09-27 | |
| dc.date | 2007-10-23 | |
| dc.date.accessioned | 2026-07-07T08:37:31Z | |
| dc.date.available | 2026-07-07T08:37:31Z | |
| dc.description | 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. | |
| dc.description | 24 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0709.4291 | |
| dc.identifier | http://arxiv.org/abs/0709.4291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140422 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 05, 20F | |
| dc.title | Affine descents and the Steinberg torus | |
| dc.type | text |