Inequalities on Bruhat graphs, R- and Kazhdan-Lusztig polynomials

DOI10.1016/J.JCTA.2012.10.001zbMATH Open1292.05269arXiv1211.4305OpenAlexW2069768408MaRDI QIDQ1930144

Masato Kobayashi

Publication date: 10 January 2013

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Abstract: From a combinatorial perspective, we establish three inequalities on coefficients of $R$- and Kazhdan-Lusztig polynomials for crystallographic Coxeter groups: (1) Nonnegativity of $(q-1)$-coefficients of $R$-polynomials, (2) a new criterion of rational singularities of Bruhat intervals by sum of quadratic coefficients of $R$-polynomials, (3) existence of a certain strict inequality (coefficientwise) of Kazhdan-Lusztig polynomials. Our main idea is to understand Deodhar's inequality in a connection with a sum of $R$-polynomials and edges of Bruhat graphs.

Full work available at URL: https://arxiv.org/abs/1211.4305

zbMATH Keywords

Coxeter groupsKazhdan-Lusztig polynomialsBruhat graphsR-polynomials

Mathematics Subject Classification ID

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