Skip to Main content Skip to Navigation
Conference papers

Schubert varieties, inversion arrangements, and Peterson translation

Abstract : We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+1)$ of the coexponents $d_1,\ldots,d_l$ is equal to the size of the Bruhat interval [e,w]. We also use Peterson translation of coconvex sets to give a Shapiro-Steinberg-Kostant rule for the exponents of $\mathcal{w}$.
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/hal-01207554
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, October 1, 2015 - 9:28:17 AM
Last modification on : Wednesday, August 7, 2019 - 12:19:20 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:38:46 AM

File

dmAT0162.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

William Slofstra. Schubert varieties, inversion arrangements, and Peterson translation. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.715-726, ⟨10.46298/dmtcs.2436⟩. ⟨hal-01207554⟩

Share

Metrics

Record views

152

Files downloads

457