论文标题
lie superalgebras $ \ mathfrak {sl}（m | n）$或$ \ mathfrak {osp}（m | 2n）$
Centres of centralizers of nilpotent elements in Lie superalgebras $\mathfrak{sl}(m|n)$ or $\mathfrak{osp}(m|2n)$
论文作者
论文摘要
令$ \ bar {g} $为简单的代数超组$ \ mathrm {sl}（m | n）$或$ \ mathrm {osp}（m | 2n）$ over $ \ mathbb {c} $。令$ \ Mathfrak {g} = \ Mathrm {lie}（\ bar {g}）= \ Mathfrak {g} _ {\ bar {0}} \ oplus \ mathfrak {g} $ \ mathbb {c} $被认为是偶数集中的超级巨头。假设$ e \ in \ mathfrak {g} _ {\ bar {0}} $是nilpotent。我们描述了$ \ mathfrak {g} $ in $ e $的centralizer $ \ mathfrak {g}^{e} $及其中心$ \ mathfrak {z}（\ mathfrak {g}^e}）$。特别是，我们给出了$ \ mathfrak {g}^{e} $，$ \ mathfrak {z}（\ Mathfrak {\ mathfrak {g}^{e}）$和$ \ left（\ mathfrak {z}（\ mathfrak {g}^e} {e} {我们还针对$ e $确定了标记的dynkin图$ \ vardelta $，然后描述$ \ left（\ mathfrak {z}（\ mathfrak {\ mathfrak {g}^{e} {e}）\ right）\ right）
Let $\bar{G}$ be the simple algebraic supergroup $\mathrm{SL}(m|n)$ or $\mathrm{OSp}(m|2n)$ over $\mathbb{C}$. Let $\mathfrak{g}=\mathrm{Lie}(\bar{G})=\mathfrak{g}_{\bar{0}}\oplus\mathfrak{g}_{\bar{1}}$ and let $G=\bar{G}(\mathbb{C})$ where $\mathbb{C}$ is considered as a superalgebra concentrated in even degree. Suppose $e\in\mathfrak{g}_{\bar{0}}$ is nilpotent. We describe the centralizer $\mathfrak{g}^{e}$ of $e$ in $\mathfrak{g}$ and its centre $\mathfrak{z}(\mathfrak{g}^{e})$. In particular, we give bases for $\mathfrak{g}^{e}$, $\mathfrak{z}(\mathfrak{g}^{e})$ and $\left(\mathfrak{z}(\mathfrak{g}^{e})\right)^{G^{e}}$. We also determine the labelled Dynkin diagram $\varDelta$ with respect to $e$ and subsequently describe the relation between $\left(\mathfrak{z}(\mathfrak{g}^{e})\right)^{G^{e}}$ and $\varDelta$.
