Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties

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dc.creatorLascoux, Alain
dc.creatorLeclerc, Bernard
dc.creatorThibon, Jean-Yves
dc.date1995-12-27
dc.date.accessioned2026-07-07T09:16:47Z
dc.date.available2026-07-07T09:16:47Z
dc.descriptionWe introduce a new family of symmetric functions, which are $q$-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine algebra of type $A_{n-1}^{(1)}$ and are related to Hall-Littlewood functions via the geometry of flag varieties. We present a series of conjectures, and prove them in special cases. The essential step in proving that these functions are actually symmetric consists in the calculation of a basis of highest weight vectors of the $q$-Fock space using ribbon tableaux.
dc.description35 pages, latex, epic and eepic macros
dc.identifierhttps://arxiv.org/abs/q-alg/9512031
dc.identifierhttp://arxiv.org/abs/q-alg/9512031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153479
dc.subjectQuantum Algebra
dc.titleRibbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties
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