Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11016752 | Journal of Algebra | 2019 | 59 Pages |
Abstract
Let (W,S) be a finite Coxeter system with root system R and with set of positive roots R+. For αâR, v,wâW, we denote by âα, âw and âw/v the divided difference operators and skew divided difference operators acting on the coinvariant algebra of W. Generalizing the work of Liu [15], we prove that âw/v can be written as a polynomial with nonnegative coefficients in âα where αâR+. In fact, we prove the stronger and analogous statement in the Nichols-Woronowicz algebra model for Schubert calculus on W after Bazlov [4]. We draw consequences of this theorem on saturated chains in the Bruhat order, and partially treat the question when âw/v can be written as a monomial in âα where αâR+. In an appendix, we study related combinatorics on shuffle elements and Bruhat intervals of length two.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Christoph Bärligea,