Parking functions and vertex operators
Vladimir Dotsenko's (University of Dublin)
Wednesday 23rd January, 2008 16:00-17:00 Mathematics Building, room 214
We use representation theory of some infinite-dimensional algebras (which are lattice vertex operator algebras for some particular lattice Heisenberg algebras) to construct multi-graded vector spaces whose characters are equal to Frobenius characters of the spaces of parking functions. We also state and discuss conjectures relating these spaces to spaces of global sections of some coherent sheaves on zero fibers of Hilbert schemes.