2022/04/25 by Suho Oh, Oh, Suho, Edward Richmond +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2204.11959
In this paper, we study the decomposition of Bruhat intervals in a Coxeter group with respect to cosets of a parabolic subgroup. Our main result is that the intersection of a lower Bruhat interval with a parabolic coset contains a unique maximal element. As an application, we give a decomposition formula for the Poincaré polynomial of a Coxeter group element. We also show that the fibers of standard parabolic projection maps on Schubert varieties are themselves Schubert varieties.