Affine descents and the Steinberg torus
Abstrak
Let $W \ltimes L$ be an irreducible affine Weyl group with Coxeter complex $\Sigma$, 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 $\Sigma$ 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 $\gamma$-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.
Topik & Kata Kunci
Penulis (3)
Kevin Dilks
T. Kyle Petersen
John R. Stembridge
Akses Cepat
- Tahun Terbit
- 2008
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.3631
- Akses
- Open Access ✓