Categorification of tensor product representations of slk and category O
Categorification of tensor product representations of slk and category O
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DOI：
10.1016/j.jalgebra.2014.12.043
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发表时间：
2014-07
影响因子：
0.9
通讯作者：
Antonio Sartori;C. Stroppel
中科院分区：
文献类型：
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作者：
Antonio Sartori;C. Stroppel
我们在推广Sussan和Mazorchuk-Stroppel之前的工作的基础上，构造了任意有限维不可约的sl k的具有BGG范畴O的子商范畴的张量积的范畴。利用李理论方法，我们详细证明了它们是Losev和Webster最近定义意义上的张量积范畴。作为一种应用，我们推导出范畴O的某些版本与韦伯斯特张量积范畴之间的范畴等价。最后，我们指出了gl （1 bb0 1）的自然表示的张量积的分类是如何适应这个框架的。
We construct categorifications of tensor products of arbitrary finite-dimensional irreducible representations of sl k with subquotient categories of the BGG category O, generalizing previous work of Sussan and Mazorchuk–Stroppel. Using Lie theoretical methods, we prove in detail that they are tensor product categorifications in the sense of the recent definition of Losev and Webster. As an application we deduce an equivalence of categories between certain versions of category O and Webster's tensor product categories. Finally we indicate how the categorifications of tensor products of the natural representation of gl (1| 1) fit into this framework.