Quantum Affine Algebras, Graded Limits and Flags
Quantum Affine Algebras, Graded Limits and Flags
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DOI：
10.1007/s41745-022-00308-x
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发表时间：
2022-04
影响因子：
2.3
通讯作者：
Matheus Brito;Vyjayanthi Chari;Deniz Kus;R. Venkatesh
中科院分区：
文献类型：
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作者：
Matheus Brito;Vyjayanthi Chari;Deniz Kus;R. Venkatesh
在这篇综述中，我们回顾了（无扭）量子仿射代数的表示理论和当前代数的表示理论之间的一些最近的联系。我们主要集中在这些代数的有限维表示。这种联系是通过量子仿射代数有限维表示的分次极限和经典极限的概念而产生的。我们解释了这项研究如何导致有趣的连接与麦克唐纳多项式，并讨论了BGG型互惠的结果。我们还讨论了Demazure模块在这一理论中的作用，以及Demazure模块的表示，结构和组合学的一些最新结果。
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations of these algebras. This connection arises via the notion of the graded and classical limit of finite-dimensional representations of quantum affine algebras. We explain how this study has led to interesting connections with Macdonald polynomials and discuss a BGG-type reciprocity result. We also discuss the role of Demazure modules in this theory and several recent results on the presentation, structure and combinatorics of Demazure modules.