The -crystal combinatorics of higher level Fock spaces
Thomas Gerber
RWTH Aachen, GermanyEmily Norton
Max Planck Institute for Mathematics, Bonn, Germany
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Abstract
For integers , the level Fock space has an -crystal structure arising from the action of a Heisenberg algebra, intertwining the -crystal. The vertices of these crystals are charged -partitions. We give the combinatorial rule for computing the arrows anywhere in the -crystal. This allows us to pinpoint the location of any charged -partition. As an application, we compute the support of the spherical representation of a cyclotomic rational Cherednik algebra, and in particular, the set of parameters such that it is finite-dimensional. We also give an easy abacus characterization of all finite-dimensional representations of type Cherednik algebras.
Cite this article
Thomas Gerber, Emily Norton, The -crystal combinatorics of higher level Fock spaces. J. Comb. Algebra 2 (2018), no. 2, pp. 103–145
DOI 10.4171/JCA/2-2-1