论文标题
在修改的固定非典型性的扩展图上
On modified extension graphs of a fixed atypicality
论文作者
论文摘要
在本文中，我们研究了经典谎言的有限维简单模块$ \ mathfrak {gl}（m | n），\ mathfrak {osp}（m | 2n）$和$ \ mathfrak {q} _m $。我们考虑通过识别通过奇偶校验更改和删除循环获得的表示形式来从$ ext^1 $ graph产生的扩展图的简化版本。我们给出了连接一对顶点的必要条件，并在大多数情况下表明这种情况就足够了。这种条件意味着在duflo-serganova函子下有限维简单模块的图像具有不可分解的同种型组件。这产生了（\ Mathfrak {gl}（m | n））$的$ \ mathcal {f}的duflo-serganova functor和$ \ mathcal {f} in（\ mathfrak {osp {osp}（m | 2n））$。
In this paper we study extensions between finite-dimensional simple modules over classical Lie superalgebras $\mathfrak{gl}(m|n), \mathfrak{osp}(M|2n)$ and $\mathfrak{q}_m$. We consider a simplified version of the extension graph which is produced from the $Ext^1$-graph by identifying representations obtained by parity change and removal of the loops. We give a necessary condition for a pair of vertices to be connected and show that this condition is sufficient in most of the cases. This condition implies that the image of a finite-dimensional simple module under the Duflo-Serganova functor has indecomposable isotypical components. This yields semisimplicity of Duflo-Serganova functor for $\mathcal{F}in(\mathfrak{gl}(m|n))$ and for $\mathcal{F}in(\mathfrak{osp}(M|2n))$.
