论文标题
在Schur-Weyl二元性的超级动物上
On a super-analog of the Schur-Weyl Duality
论文作者
论文摘要
考虑了Schur-weyl二元性的两个超级分析：$（\ Mathbb {C}^{M | n}）中的动作二元性二元性二元性二元性二元性，lie superalgebra $ \ mathfrak {gl}（gl}（gl}（gl}（m，n）$）和对称的$ s_n $ s_ $ s_n $ s y lie qu q y q y q y qu q y q y qu q y q y q y q y q y qu q以及$（\ mathbb {c}^{n | n}）^{\ otimes n} $中的某个有限组$ se（n）$。我们构建了这些谎言超级对称代数的对称和普遍包围代数的同构，称为特殊对称。使用这种向量空间的同构，我们明确描述了相应的通用包围代数和组代数的中心之间的二元性。
Two super-analogs of the Schur-Weyl duality are considered: the duality of actions in $(\mathbb{C}^{m|n})^{\otimes N}$ of the Lie superalgebra $\mathfrak{gl}(m,n)$ and the symmetric group $S_N$, and the duality of actions of the Lie superalgebra $Q(n)$ and a certain finite group $Se(N)$ in $(\mathbb{C}^{n|n})^{\otimes N}$. We construct an isomorphism of symmetric and universal enveloping algebras of these Lie superalgebras called special symmetrization. Using this isomorphism of vector spaces we describe explicitly the duality between the centers of the corresponding universal enveloping algebras and the group algebras.
