论文标题
基本经典谎言超级甲虫的有界重量模块在无穷大
Bounded weight modules for basic classical Lie superalgebras at infinity
论文作者
论文摘要
我们对复杂简单的简单谎言$ \ mathfrak {sl}（\ infty | \ infty）$和$ \ mathfrak {osp}（m | 2n）$进行了对简单的重量模块进行分类。对于$ \ mathfrak {osp}（m | 2n）$，此类模块是旋转器类型的类型，即，它们将其组合成已知类别的纺纱$ \ mathfrak {o}（M）$ - $ - $ sciLLator-type-type type $ \ mathfrak $ \ mathfrak {sp}（sp}（2n）$ - 模块。此外，我们表征了$ \ mathfrak {osp}（m | 2n）$（在假设$ \ dim \，\ mathfrak，\ mathfrak {osp}（m | 2n）= \ infty $）上，通过将其研究降低到已知的已知类别的$ \ m m mathfrak $ n $ n， $ \ infty $。当对简单有限的重量分类$ \ mathfrak {sl}（\ infty | \ infty）$ - 模块时，我们证明，每个此类模块都可以集成在两个无限二维理想之一中，这是lie代数$ \ mathfrak {sl} {sl}（\ infty | \ infty | \ iffty）_ {\ bar} = 0} $ {0} $ {0}。我们通过建立一些有关有限权重$ \ mathfrak {sl}（\ infty | \ infty）$ - 模块的第一个事实来完成论文。
We classify simple bounded weight modules over the complex simple Lie superalgebras $\mathfrak{sl}(\infty |\infty)$ and $\mathfrak{osp} (m | 2n)$, when at least one of $m$ and $n$ equals $\infty$. For $\mathfrak{osp} (m | 2n)$ such modules are of spinor-oscillator type, i.e., they combine into one the known classes of spinor $\mathfrak{o} (m)$-modules and oscillator-type $\mathfrak{sp} (2n)$-modules. In addition, we characterize the category of bounded weight modules over $\mathfrak{osp} (m | 2n)$ (under the assumption $\dim \, \mathfrak{osp} (m | 2n) = \infty$) by reducing its study to already known categories of representations of $\mathfrak{sp} (2n)$, where $n$ possibly equals $\infty$. When classifying simple bounded weight $\mathfrak{sl}(\infty |\infty)$-modules, we prove that every such module is integrable over one of the two infinite-dimensional ideals of the Lie algebra $\mathfrak{sl}(\infty |\infty)_{\bar{0}}$. We finish the paper by establishing some first facts about the category of bounded weight $\mathfrak{sl} (\infty |\infty)$-modules.
