Parking functions and vertex operators

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dc.creatorDotsenko, Vladimir
dc.date2008-09-22
dc.date2008-12-09
dc.date.accessioned2026-07-07T12:49:44Z
dc.date.available2026-07-07T12:49:44Z
dc.descriptionWe introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct series of vector spaces whose dimensions are Catalan numbers and Fuss--Catalan numbers respectively. Conjecturally, these spaces are related to spaces of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras.
dc.description17 pages, 1 figure, proofs are made more detailed. To appear in Selecta Mathematica
dc.identifierhttps://arxiv.org/abs/0809.3683
dc.identifierhttp://arxiv.org/abs/0809.3683
dc.identifierSelecta Math. 14: 2 (2009), 229-245
dc.identifierdoi:10.1007/s00029-008-0067-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222477
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject17B69 (Primary) 05E05, 20C30 (Secondary)
dc.titleParking functions and vertex operators
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