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Universal Verma Modules and the Misra-Miwa Fock Space

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  • Arun Ram
  • Peter Tingley

Abstract

The Misra-Miwa -deformed Fock space is a representation of the quantized affine algebra . 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 . Partitions also index the polynomial Weyl modules for as tends to infinity. We explain how the powers of 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.

Suggested Citation

  • Arun Ram & Peter Tingley, 2010. "Universal Verma Modules and the Misra-Miwa Fock Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-19, January.
    • Handle: RePEc:hin:jijmms:326247
    DOI: 10.1155/2010/326247
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