%0 Journal Article
%T Universal Verma modules and the Misra-Miwa Fock space
%A Arun Ram
%A Peter Tingley
%J Mathematics
%D 2010
%I arXiv
%X 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
%U http://arxiv.org/abs/1002.0558v2