Parking functions and vertex operators

Details Parking functions and vertex operators Parking functions and vertex operators

2008-09-22

arxiv.org/abs/0809.3683v2

Selecta Math. 14: 2 (2009), 229-245

Mathematics

Representation Theory

17 pages, 1 figure, proofs are made more detailed. To appear in Selecta Mathematica

Scientific paper

10.1007/s00029-008-0067-7

We 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.

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