论文标题
二元性和动态WEYL群
Howe duality and dynamical Weyl group
论文作者
论文摘要
我们给出了$ u_q（\ wideHat {\ mthfrak {\ mathfrak {gl}} _ n）$的外部功能的$ r $ $ - matricuse的效率公式（$ \ mathfrak {gl} _n，\ mathfrak {gl} _m）$ - 偶性。在限制$ n \ to \ infty $中，我们获得了fock空间的$ r $ $ - matrices。由于我们的结果，我们获得了Weyl组在可集成的$ u_q \ mathfrak {gl} _m $ -Modules上的动态动作，从而扩展了已知的动作在零重量空间上。在Anfisa Gurenkova的附录中，表明如果我们用一般的同样对称的kac-moody代数替换$ \ mathfrak {gl} _m $，则后者也将持有。
We give a fermionic formula for $R$-matrices of exterior powers of the vector representations of $U_q(\widehat{ \mathfrak{gl}}_N)$ and relate it to the dynamical Weyl group of Tarasov--Varchenko and Etingof--Varchenko, via a Howe ($\mathfrak{gl}_N,\mathfrak{gl}_M)$-duality. In the limit $N\to\infty$ we obtain $R$-matrices for Fock spaces. As a consequence of our result we obtain a dynamical action of the Weyl group on integrable $U_q\mathfrak{gl}_M$-modules, extending the known action on zero weight spaces. In an Appendix by Anfisa Gurenkova it is shown that the latter property also holds if we replace $\mathfrak{gl}_M$ by a general symmetrizable Kac--Moody algebra.
