Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras

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dc.creatorSavage, Alistair
dc.date2006-01-20
dc.date.accessioned2026-07-07T08:48:25Z
dc.date.available2026-07-07T08:48:25Z
dc.descriptionKashiwara and Saito have defined a crystal structure on the set of irreducible components of Lusztig's quiver varieties. This gives a geometric realization of the crystal graph of the lower half of the quantum group associated to a simply-laced Kac-Moody algebra. Using an enumeration of the irreducible components of Lusztig's quiver varieties in finite and affine type A by combinatorial data, we compute the geometrically defined crystal structure in terms of this combinatorics. We conclude by comparing the combinatorial realization of the crystal graph thus obtained with other combinatorial models involving Young tableaux and Young walls.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0601511
dc.identifierhttp://arxiv.org/abs/math/0601511
dc.identifierLie algebras, vertex operator algebras and their applications (Raleigh, NC, 2005), 221-232, Contemp. Math., 442, Amer. Math. Soc., Providence, RI, 2007.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143940
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject16G20, 17B37
dc.titleGeometric and Combinatorial Realizations of Crystals of Enveloping Algebras
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