Universal Verma modules and the Misra-Miwa Fock space

Abstract

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 $U_q(g{l}_N)$ 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

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

References in corpus (4)

• 2-Kac-Moody algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Graded decomposition matrices of v-Schur algebras via Jantzen filtration
• The b-functions for prehomogeneous vector spaces of commutative parabolic type and generalized universal Verma modules

Cited by in corpus (1)

• Graded decomposition matrices of v-Schur algebras via Jantzen filtration