Parking functions and vertex operators

Dotsenko, Vladimir (2008) Parking functions and vertex operators. Selecta Mathematica, 14 (2). pp. 229-245. ISSN 1022-1824

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Abstract

We introduce several associative algebras and families of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we define a family of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct families 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.

Item Type:	Article
Divisions:	School of Theoretical Physics > Preprints
Date Deposited:	05 Oct 2017 19:18
Last Modified:	17 Dec 2022 10:07
URI:	https://dair.dias.ie/id/eprint/230

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