The Misra-Miwa $v$-deformed Fock space is a representation of the quantized
affine algebra of type A. 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 the quantum group $U_q(gl_N)$ 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