Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements

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dc.creatorJones, Brant C.
dc.date2007-11-09
dc.date.accessioned2026-07-07T08:41:50Z
dc.date.available2026-07-07T08:41:50Z
dc.descriptionWe show that the leading coefficient of the Kazhdan--Lusztig polynomial $P_{x,w}(q)$ known as $μ(x,w)$ is always either 0 or 1 when $w$ is a Deodhar element of a finite Weyl group. The Deodhar elements have previously been characterized using pattern avoidance by Billey--Warrington (2001) and Billey--Jones (2007). In type $A$, these elements are precisely the 321-hexagon avoiding permutations. Using Deodhar's (1990) algorithm, we provide some combinatorial criteria to determine when $μ(x,w) = 1$ for such permutations $w$.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0711.1391
dc.identifierhttp://arxiv.org/abs/0711.1391
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141800
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject20C08
dc.titleLeading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements
dc.typetext

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