论文标题
Gelfand- Graev functor和Quantum Aggine Schur- weyl二元性
Gelfand--Graev functor and quantum affine Schur--Weyl duality
论文作者
论文摘要
我们阐明了Gelfand（Graev模块的中央覆盖物）之间的关系，Euler-poincaré的Arnold- brieskorn歧管的多项式和量子仿射Schur- weyl二元性。这三个对象及其关系由Weyl群的置换表示决定。 具体来说，我们的主要结果表明，对于$ \ mathrm {gl}（r）的某些封面，gelfand-graev functor与量子仿射schur - weyl二元性有关。因此，Gelfand的Iwahori固定部分的通勤代数 - Graev代表是量子群的商。
We explicate relations among the Gelfand--Graev modules for central covers, the Euler--Poincaré polynomial of the Arnold--Brieskorn manifold, and the quantum affine Schur--Weyl duality. These three objects and their relations are dictated by a permutation representation of the Weyl group. Specifically, our main result shows that for certain covers of $\mathrm{GL}(r)$ the Gelfand--Graev functor is related to quantum affine Schur--Weyl duality. Consequently, the commuting algebra of the Iwahori-fixed part of the Gelfand--Graev representation is the quotient of a quantum group.
