论文标题
量子仿射代数，分级限制和标志
Quantum affine algebras, graded limits, and flags
论文作者
论文摘要
在这项调查中，我们回顾了（未介绍）量子仿射代数的表示理论与当前代数的表示理论之间的一些最新联系。我们主要关注这些代数的有限维表示。这种联系是通过量子仿射代数的有限维表示的分级和经典限制的概念而产生的。我们解释了这项研究如何导致与麦克唐纳多项式的有趣联系，并讨论了BGG型互惠结果。我们还讨论了项中的启示模块在该理论中的作用，以及有关氮杂模块的呈现，结构和组合的最新结果。
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.
