论文标题
通用线性超级组的Donkin-Koppinen过滤的组合方法
A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups
论文作者
论文摘要
对于一般线性超级组$ g = gl（m | n）$，我们认为天然的同构$ ϕ：g \ to u^ - \ times g_ {ev} \ times u^+$，其中$ g_ {ev ev} $是$ g $的$ g $，$ u^ - $ u^ - $ u^ - $ u^+$ g $ g $ g $ g $ g $ g $ g $ g $ umiptent of $ g $。我们计算出$ k [g] $的生成器的奇数偏远分化的动作$ ϕ^*（x_ {ij}）$。 我们描述了$ gl（m | n）$的主要权重$ x（t）^+$的特定顺序，其中存在坐标代数$ k [g] $的Donkin-Koppinen过滤。令$γ$成为有限生成的理想$γ$的$ x（t）^+$和$o_γ（k [g]）$是最大的$γ$ -subsupermodule $ k [g] $具有最高权重的简单组成因子$λ\ inγ$。我们使用通用的二键剂应用组合技术来确定$o_γ（k [g]）$的Donkin-Koppinen过滤中出现的$ g $ -superbimodules的基础。
For a general linear supergroup $G=GL(m|n)$, we consider a natural isomorphism $ϕ: G \to U^-\times G_{ev} \times U^+$, where $G_{ev}$ is the even subsupergroup of $G$, and $U^-$, $U^+$ are appropriate odd unipotent subsupergroups of $G$. We compute the action of odd superderivations on the images $ϕ^*(x_{ij})$ of the generators of $K[G]$. We describe a specific ordering of the dominant weights $X(T)^+$ of $GL(m|n)$ for which there exists a Donkin-Koppinen filtration of the coordinate algebra $K[G]$. Let $Γ$ be a finitely generated ideal $Γ$ of $X(T)^+$ and $O_Γ(K[G])$ be the largest $Γ$-subsupermodule of $K[G]$ having simple composition factors of highest weights $λ\in Γ$. We apply combinatorial techniques, using generalized bideterminants, to determine a basis of $G$-superbimodules appearing in Donkin-Koppinen filtration of $O_Γ(K[G])$.
