2019/04/24 by Robert Mcalmon, Mcalmon, Robert, Suho Oh +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1904.11048
openalex publication_date 2019/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An element w of the Weyl group is called rationally smooth if the corresponding Schubert variety is rationally smooth. This happens exactly when the lower interval [id,w] in the Bruhat order is palindromic. For each element w of the Weyl group, we construct a certain hyperplane arrangement. After analyzing the palindromic intervals inside the maximal quotients, we use this result to show that the generating function for regions of the arrangement coincides with the Poincaré polynomial of the corresponding Schubert variety if and only if the Schubert variety is rationally smooth.