Affine Stanley symmetric functions

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dc.creatorLam, Thomas
dc.date2005-01-21
dc.date.accessioned2026-07-07T05:16:14Z
dc.date.available2026-07-07T05:16:14Z
dc.descriptionWe define a new family of symmetric functions which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric functions generalise the (dual of the) $k$-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. Conjecturally, affine Stanley symmetric functions should be related to the cohomology of the affine flag variety.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0501335
dc.identifierhttp://arxiv.org/abs/math/0501335
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73907
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject05E05
dc.titleAffine Stanley symmetric functions
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