论文标题
表示理论的介绍
IntroSurvey of representation theory
论文作者
论文摘要
鉴于它是一个巨大的领域，可能会有成千上万的代表理论介绍/调查。这只是其中之一，非常个人化和非正式。它的难度越来越高；第一部分旨在用于最后一年的本科生。我们解释了表示理论的一些基本知识，特别是Schur-Weyl二元性和对称群体的表示。然后，我们进行量子版本，介绍Kazhdan-Lusztig理论，量子组及其分类版本。然后，我们继续对模块化表示理论的一些最新进展进行调查。我们结束了二十个开放问题和一首绝望的歌。
There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of difficulty; the first part is intended for final year undergrads. We explain some basics of representation theory, notably Schur-Weyl duality and representations of the symmetric group. We then do the quantum version, introduce Kazhdan-Lusztig theory, quantum groups and their categorical versions. We then proceed to a survey of some recent advances in modular representation theory. We finish with twenty open problems and a song of despair.
