Universal Verma Modules and the Misra-Miwa Fock Space
Name
Ram-2010-Universal Verma Modules and the Misra.pdf
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705.01 KB
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Author(s)
Tingley, Peter William
Ram, Arun
Date Issued
November 2010
Journal
International Journal of Mathematics and Mathematical Sciences
Publisher
Hindawi Pub. Corp.
Citation
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.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1155/2010/326247
