The Horn recursion for Schur P- and Q- functions: Extended Abstract

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dc.creatorPurbhoo, Kevin
dc.creatorSottile, Frank
dc.date2006-03-08
dc.date.accessioned2026-07-07T07:06:38Z
dc.date.available2026-07-07T07:06:38Z
dc.descriptionA consequence of work of Klyachko and of Knutson-Tao is the Horn recursion to determine when a Littlewood-Richardson coefficient is non-zero. Briefly, a Littlewood-Richardson coefficient is non-zero if and only if it satisfies a collection of Horn inequalities which are indexed by smaller non-zero Littlewood-Richardson coefficients. There are similar Littlewood-Richardson numbers for Schur P- and Q- functions. Using a mixture of combinatorics of root systems, combinatorial linear algebra in Lie algebras, and the geometry of certain cominuscule flag varieties, we give Horn recursions to determine when these other Littlewood-Richardson numbers are non-zero. Our inequalities come from the usual Littlewood-Richardson numbers, and while we give two very different Horn recursions, they have the same sets of solutions. Another combinatorial by-product of this work is a new Horn-type recursion for the usual Littlewood-Richardson coefficients.
dc.description9 pages, extended abstract for FPSAC06 conference
dc.identifierhttps://arxiv.org/abs/math/0603180
dc.identifierhttp://arxiv.org/abs/math/0603180
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110101
dc.subjectCombinatorics
dc.subjectAlgebraic Geometry
dc.subject05E15; 14M15
dc.titleThe Horn recursion for Schur P- and Q- functions: Extended Abstract
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