Large annihilator category O for sl_{\infty}, o_{\infty}, sp_{\infty}.
Large annihilator category O for sl_{\infty}, o_{\infty}, sp_{\infty}.
复制标题
sl_{infty}、o_{infty}、sp_{infty} 的大歼灭子类别 O。
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
V. Serganova
中科院分区：
文献类型：
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作者：
I. Penkov;V. Serganova
对于无限维李代数$\fg=\mathfrak{sl}(\infty),\mathfrak{o}(\infty), \mathfrak{sp}(\infty)$，我们构造了一个新的BGG范畴$\mathcal O$的类似物。与\cite{Nam}和\cite{CP}中研究的类别的一个主要区别是，我们的类别的所有对象都满足\cite{DPS}中引入的大湮灭子条件。尽管事实上，$\fg$的分裂Borel子代数$\fb$不是共轭的，但我们可以消除对$\fb$的选择的依赖，并引入一个普遍的最高权重类别$\mathcal {OLA}$$\fg$ -模块，字母$\mathcal{LA}$来自“大湮灭子”。$\mathcal {OLA}$中可积对象的子范畴正是\cite{DPS}中研究的$\mathbb T_{\fg}$范畴。我们研究了$\mathcal {OLA}$的结构，特别是计算了标准对象中简单对象的多重性和不可分解注入中标准对象的多重性。
We construct a new analogue of the BGG category $\mathcal O$ for the infinite-dimensional Lie algebras $\fg=\mathfrak{sl}(\infty),\mathfrak{o}(\infty), \mathfrak{sp}(\infty)$. A main difference with the categories studied in \cite{Nam} and \cite{CP} is that all objects of our category satisfy the large annihilator condition introduced in \cite{DPS}. Despite the fact that the splitting Borel subalgebras $\fb$ of $\fg$ are not conjugate, one can eliminate the dependency on the choice of $\fb$ and introduce a universal highest weight category $\mathcal {OLA}$ of $\fg$-modules, the letters $\mathcal{LA}$ coming from "large annihilator". The subcategory of integrable objects in $\mathcal {OLA}$ is precisely the category $\mathbb T_{\fg}$ studied in \cite{DPS}. We investigate the structure of $\mathcal {OLA}$, and in particular compute the multiplicities of simple objects in standard objects and the multiplicities of standard objects in indecomposable injectives.