论文标题
GL（M | N）和广义Schur Superalgebras的Donkin-Koppinen过滤
Donkin-Koppinen filtration for GL(m|n) and generalized Schur superalgebras
论文作者
论文摘要
该论文包含的结果表征了一般线性超级组$ g = gl（m | n）$的坐标超级级$ k [g] $c_γ=o_γ（k [g]）$的结果。在这里，超模块$c_γ$是$ k [g] $的最大的子模块，其组成因子是不可约的超级模型，最高权重$λ$，其中$λ$属于有限生成的理想$γ$的poset $ x（t）^+g $ g $的poset $ x（t）^+$ g $。 $ g $的分解作为usuperschemes $ u^ - \ times g_ {ev} \ times u^+$诱导superalgebra isomorphism $ ϕ^*：k [u^ - ] \ otimes k [g_ {ev}我们表明$c_γ= ϕ^*（k [u^ - ] \ otimesm_γ\ otimes k [u^+]）$，其中$m_γ=o_γ（k [g_ {ev}]）$。使用通用的二键剂给出的模块$M_γ$的基础，我们描述了$C_γ$的基础。 由于每个$c_γ$都是$ k [g] $的子菜单，其双$c_γ^*=s_γ$是一个（pseudoCompact）Superalgebra，称为广义Schur Superalgebra。有一个自然的超级级摩尔词$π_γ：dist（g）\ tos_γ$，使得分布代数$ dist（g）$的图像在$s_γ$中密集。对于理想的$ x（t）^+_ {l} $，固定长度的所有权重，描述了$π_{x（t）^+_ {l}} $的内核的生成器。
The paper contains results that characterize the Donkin-Koppinen filtration of the coordinate superalgebra $K[G]$ of the general linear supergroup $G=GL(m|n)$ by its subsupermodules $C_Γ=O_Γ(K[G])$. Here, the supermodule $C_Γ$ is the largest subsupermodule of $K[G]$ whose composition factors are irreducible supermodules of highest weight $λ$, where $λ$ belongs to a finitely-generated ideal $Γ$ of the poset $X(T)^+$ of dominant weights of $G$. A decomposition of $G$ as a product of subsuperschemes $U^-\times G_{ev}\times U^+$ induces a superalgebra isomorphism $ϕ^* : K[U^-]\otimes K[G_{ev}]\otimes K[U^+]\simeq K[G]$. We show that $C_Γ=ϕ^*(K[U^-]\otimes M_Γ\otimes K[U^+])$, where $M_Γ=O_Γ(K[G_{ev}])$. Using the basis of the module $M_Γ$, given by generalized bideterminants, we describe a basis of $C_Γ$. Since each $C_Γ$ is a subsupercoalgebra of $K[G]$, its dual $C_Γ^*=S_Γ$ is a (pseudocompact) superalgebra, called the generalized Schur superalgebra. There is a natural superalgebra morphism $π_Γ:Dist(G)\to S_Γ$ such that the image of the distribution algebra $Dist(G)$ is dense in $S_Γ$. For the ideal $X(T)^+_{l}$, of all weights of fixed length $l$, the generators of the kernel of $π_{X(T)^+_{l}}$ are described.
