Kashiwara and Zelevinsky involutions in affine type A

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dc.creatorJacon, Nicolas
dc.creatorLecouvey, Cédric
dc.date2009-01-05
dc.date2009-04-22
dc.date.accessioned2026-07-07T13:06:39Z
dc.date.available2026-07-07T13:06:39Z
dc.descriptionWe first describe how the Kashiwara involution on crystals of affine type $A$ is encoded by the combinatorics of aperiodic multisegments. This yields a simple relation between this involution and the Zelevinsky involution on the set of simple modules for the affine Hecke algebras. We then give efficient procedures for computing these involutions. Remarkably, these procedures do not use the underlying crystal structure. They also permit to match explicitly the Ginzburg and Ariki parametrizations of the simple modules associated to affine and cyclotomic Hecke algebras, respectively .
dc.description24 pages, to appear in Pacific J. Math
dc.identifierhttps://arxiv.org/abs/0901.0443
dc.identifierhttp://arxiv.org/abs/0901.0443
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227849
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject20C08;05E10;17B37
dc.titleKashiwara and Zelevinsky involutions in affine type A
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