泛韦尔马模与Misra-Miwa Fock空间
Universal Verma modules and the Misra-Miwa Fock space
摘要：
Misra-Miwa $v$ -变形的Fock空间是A型量子化仿射代数的表示。它具有由分区索引的标准基，并且Chevalley生成器关于该基的动作的非零矩阵项是$v$的幂。划分也索引量子群$U_q(gl_N)$的多项式Weyl模，因为$N$趋于无穷大。我们解释了如何权力的$v$出现在Misra-Miwa福克空间也自然出现在Weyl模的上下文中。我们使用的主要工具是普适韦尔马模的Shapovalov行列式
英文摘要：
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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