MoMonoidal categories of modules over quantum affine algebras of type A and B
MoMonoidal categories of modules over quantum affine algebras of type A and B
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A 型和 B 型量子仿射代数上模的 MoMonoidal 范畴
DOI：
10.1112/plms.12160
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Se-jin
中科院分区：
文献类型：
--
作者：
Kashiwara;Masaki;Kim;Myungho and Oh;Se-jin
我们构造了一个从型量子仿射代数上的有限维分次模范畴到型量子仿射代数上的有限维可积模范畴的正合张量函子.它通过范畴进行分解，这是一个局部化的。结果，这个函子诱导了一个从的Grothendieck环（忽略分次）到的子范畴的Grothendieck环的环同构。此外，它导致了简单对象类之间的双射。由于这一范畴与型量子仿射代数的范畴有关，我们得到了型量子仿射代数上的模范畴与型量子仿射代数上的模范畴之间的一个有趣的联系。也就是说，对于每一个，存在的Grothendieck环之间的同构和的Grothendieck环，这导致了一个简单的模类之间的双射。
We construct an exact tensor functor from the categoryof finite‐dimensional graded modules over the quiver Hecke algebra of typeto the categoryof finite‐dimensional integrable modules over the quantum affine algebra of type. It factors through the category, which is a localization of. As a result, this functor induces a ring isomorphism from the Grothendieck ring of(ignoring the gradings) to the Grothendieck ring of a subcategoryof. Moreover, it induces a bijection between the classes of simple objects. Because the categoryis related to categoriesof the quantum affine algebras of type, we obtain an interesting connection between those categories of modules over quantum affine algebras of typeand type. Namely, for each, there exists an isomorphism between the Grothendieck ring ofand the Grothendieck ring of, which induces a bijection between the classes of simple modules.