Distributive lattices defined for representations of rank two semisimple Lie algebras

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dc.creatorAlverson II, L. Wyatt
dc.creatorDonnelly, Robert G.
dc.creatorLewis, Scott J.
dc.creatorMcClard, Marti
dc.creatorPervine, Robert
dc.creatorProctor, Robert A.
dc.creatorWildberger, N. J.
dc.date2007-07-17
dc.date.accessioned2026-07-07T08:18:42Z
dc.date.available2026-07-07T08:18:42Z
dc.descriptionFor a rank two root system and a pair of nonnegative integers, using only elementary combinatorics we construct two posets. The constructions are uniform across the root systems A1+A1, A2, C2, and G2. Examples appear in Figures 3.2 and 3.3. We then form the distributive lattices of order ideals of these posets. Corollary 5.4 gives elegant quotient-of-products expressions for the rank generating functions of these lattices (thereby providing answers to a 1979 question of Stanley). Also, Theorem 5.3 describes how these lattices provide a new combinatorial setting for the Weyl characters of representations of rank two semisimple Lie algebras. Most of these lattices are new; the rest of them (or related structures) have arisen in work of Stanley, Kashiwara, Nakashima, Littelmann, and Molev. In a future paper, one author shows that the posets constructed here form a Dynkin diagram-indexed answer to a combinatorially posed classification question. In a companion paper, some of these lattices are used to explicitly construct some representations of rank two semisimple Lie algebras. This implies that these lattices are strongly Sperner.
dc.description33 pages, 17 figures and tables
dc.identifierhttps://arxiv.org/abs/0707.2421
dc.identifierhttp://arxiv.org/abs/0707.2421
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134527
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05A15 (Primary); 05E10, 17B10 (Secondary)
dc.titleDistributive lattices defined for representations of rank two semisimple Lie algebras
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