Total positivity for cominuscule Grassmannians

dc.creatorLam, Thomas
dc.creatorWilliams, Lauren
dc.date2007-10-16
dc.date.accessioned2026-07-07T08:36:33Z
dc.date.available2026-07-07T08:36:33Z
dc.descriptionIn this paper we explore the combinatorics of the non-negative part (G/P)+ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams -- certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P)+. In the classical cases, we describe Le-diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can reduce an arbitrary diagram to a Le-diagram. We give enumerative results and relate our Le-diagrams to other combinatorial objects. Surprisingly, the totally non-negative cells in the open Schubert cell of the odd and even orthogonal Grassmannians are (essentially) in bijection with preference functions and atomic preference functions respectively.
dc.description39 pages
dc.identifierhttps://arxiv.org/abs/0710.2932
dc.identifierhttp://arxiv.org/abs/0710.2932
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140103
dc.subjectCombinatorics
dc.titleTotal positivity for cominuscule Grassmannians
dc.typetext

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