Universal Verma Modules and the Misra-Miwa Fock Space
Author(s)Tingley, Peter William; Ram, Arun
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The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(sle). It has a standard basis indexed by partitions, and the nonzero 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
International Journal of Mathematics and Mathematical Sciences
Hindawi Pub. Corp.
Ram, Arun and Peter Tingley, “Universal Verma Modules and the Misra-Miwa Fock Space,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 326247, 19 pages, 2010. © 2010 Arun Ram and Peter Tingley.
Final published version