Universal Verma Modules and the Misra-Miwa Fock Space

The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(ŝl`). It has a standard basis indexed by partitions and the non-zero matrix entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial Weyl modules for Uq(glN ) as N tends to infinity. We explain how the powers of v which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules. The main tool we use is the Shapovalov determinant for a universal Verma module.