Universal Verma modules and the Misra-Miwa Fock space

Details Universal Verma modules and the Misra-Miwa Fock space Universal Verma modules and the Misra-Miwa Fock space

2010-02-02

arxiv.org/abs/1002.0558v2

International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 326247, 19 pages, 2010

Mathematics

Quantum Algebra

15 pages. v2: Minor corrections and clarifications; 4 new references

Scientific paper

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

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