2026/08/05 by Aman Dave, Taiwen Feng, Nathan Lesnevich +4
Mathematics · #math.CO #msc:06A07 #msc:05E45 #msc:20F55
26 pages, 4 figures
arxiv created 2026/08/05 · arxiv updated 2026/08/06
Let W be an arbitrary Coxeter group. The shifted Bruhat interval [w1,w2] x-1, the translate of the Bruhat interval [w1,w2] by an element x, is partially ordered by the Bruhat order of W. These posets arise from affine pavings of Richardson varieties, and in general they are neither twisted intervals nor tilted Bruhat intervals. Our main result is that the shifted lower intervals [e,w] x-1 are EL-shellable for every Coxeter group, via an explicit labeling of each cover by a reflection. Along the way we show that [e,w] x-1 is a graded poset with a unique maximum given by the Demazure product and a unique minimum given by an opposite Demazure operator that we introduce.