Integrable sl(∞)‐modules and category O for gl(m|n)
Integrable sl(∞)‐modules and category O for gl(m|n)
复制标题
gl(m|n) 的可积 sl(→)→模和类别 O
DOI：
10.1112/jlms.12176
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Serganova, Vera
中科院分区：
文献类型：
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作者：
Hoyt, Crystal;Penkov, Ivan;Serganova, Vera
我们引入并研究了依赖于子代数中某个约化的选择的可积模的新范畴。的简单对象是张量模，如前面研究的范畴[Dan-Cohen，Penkov和Serganova，Adv.Math]。289(2016)250-278]；然而，与相比，选择提供了更多的非简单模块的灵活性。然后，我们选择了两个无限维对角线块，并证明了某个内射对象实现了范畴上的范畴作用，即李超代数的积分范畴。我们证明了的基座是由投射模生成的，并显式地计算了基座滤子。我们推测，基过滤反映了范畴上的“非典型过滤程度”。我们还推测，一个自然的张量过滤是通过发送范畴的Duflo-Serganova函子产生的。对于对应于有限维模的直和，我们证明了后一猜想的一个较弱的形式。
We introduce and study new categoriesof integrable‐modules which depend on the choice of a certain reductive insubalgebra. The simple objects ofare tensor modules as in the previously studied category[Dan‐Cohen, Penkov and Serganova,Adv. Math. 289 (2016) 250–278]; however, the choice ofprovides for more flexibility of nonsimple modules incompared to. We then chooseto have two infinite‐dimensional diagonal blocks, and show that a certain injective objectinrealizes a categorical‐action on the category, the integral categoryof the Lie superalgebra. We show that the socle ofis generated by the projective modules in, and compute the socle filtration ofexplicitly. We conjecture that the socle filtration ofreflects a ‘degree of atypicality filtration’ on the category. We also conjecture that a natural tensor filtration onarises via the Duflo–Serganova functor sending the categoryto. We prove a weaker version of this latter conjecture for the direct summand ofcorresponding to finite‐dimensional‐modules.