论文标题
$ ds $ fuctor的正交谎言superalgebra的半透明性
Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra
论文作者
论文摘要
我们证明，duflo-serganova functor $ ds_x $附加到一个奇数元素$ x $ of $ \ mathfrak {osp}（m | 2n）$ is samisimple，即发送半imimple表示$ m $ m $ m $ of $ \ mathfrak {osp}（osp}（osp}（m | 2n）$， $ \ mathfrak {osp}（m-2k | 2n-2k）$，其中$ k $是$ x $的等级。我们证明了$ ds_x（l（λ））$的封闭公式，根据$λ$的弧图。
We prove that the Duflo-Serganova functor $DS_x$ attached to an odd nilpotent element $x$ of $\mathfrak{osp}(m|2n)$ is semisimple, i.e. sends a semisimple representation $M$ of $\mathfrak{osp}(m|2n)$ to a semisimple representation of $\mathfrak{osp}(m-2k|2n-2k)$ where $k$ is the rank of $x$. We prove a closed formula for $DS_x(L(λ))$ in terms of the arc diagram attached to $λ$.
