Canonical bases and higher representation theory
Canonical bases and higher representation theory
复制标题
规范基础和更高表示理论
DOI：
10.1112/s0010437x1400760x
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发表时间：
2012
影响因子：
1.8
通讯作者：
Ben Webster
中科院分区：
文献类型：
--
作者：
Ben Webster
本文发展了规范基础的一般理论，以及它们是如何在范畴化的背景下自然产生的。作为应用，我们证明了当相应的李代数是有限类型的且是单边的时，整个量子化泛包络代数中的Lusztig正则基是由范畴中不可分解的1-态射的类给出的。我们还引入了Grothendieck群对应于最低权和最高权可积表示的张量积的自然范畴。这概括了作者过去在最重要情况下的工作。
Abstract This paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the whole quantized universal enveloping algebra is given by the classes of the indecomposable 1-morphisms in a categorification when the associated Lie algebra is of finite type and simply laced. We also introduce natural categories whose Grothendieck groups correspond to the tensor products of lowest- and highest-weight integrable representations. This generalizes past work of the author’s in the highest-weight case.