论文标题
与对称对相关的通勤方案的商
Quotients of commuting schemes associated to Symmetric Pairs
论文作者
论文摘要
令$ \ mathfrak {g} = \ mathfrak {g} _0 \ oplus \ mathfrak {g} _1 $ be a $ \ mathbb z_2 $ - 经典谎言algebra的grading grading $（\ mathfrak {g}，\ mathfrak}，\ mathfrak {g} _0）令$ g $为一个古典群体，带有lie代数$ \ mathfrak {g} $，让$ g_0 $为$ g $的连接子组，$ {\ rm lie}（g_0）= \ mathfrak g_0 $。对于$ d \ geq 2 $，令$ \ mathfrak {c}^d（\ mathfrak {g} _1）$为$ d $ -th通勤方案与对称对$（\ mathfrak g，\ mathfrak g，\ mathfrak g_0）$相关。在本文中，我们通过Chevalley限制性图研究了分类商$ \ mathfrak {c}^d（\ mathfrak {g} _1）// {g_0} $。结果，我们表明，分类商方案$ \ mathfrak c^d（\ mathfrak g_1）// g_0 $是正常且减少的。作为证明的一部分，我们描述了一个具有独立关注的代数$ k [\ mathfrak {g} _1^d]^{g_0} $的生成集。
Let $\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ be a $\mathbb Z_2$-grading of a classical Lie algebra such that $(\mathfrak{g}, \mathfrak{g}_0)$ is a classical symmetric pair. Let $G$ be a classical group with Lie algebra $\mathfrak{g}$ and let $G_0$ be the connected subgroup of $G$ with ${\rm Lie} (G_0)=\mathfrak g_0$. For $d \geq 2$, let $\mathfrak{C}^d(\mathfrak{g}_1)$ be the $d$-th commuting scheme associated with the symmetric pair $(\mathfrak g, \mathfrak g_0)$. In this article, we study the categorical quotient $\mathfrak{C}^d(\mathfrak{g}_1)//{G_0}$ via the Chevalley restriction map. As a consequence we show that the categorical quotient scheme $\mathfrak C^d(\mathfrak g_1)//G_0$ is normal and reduced. As a part of the proof, we describe a generating set for the algebra $k[\mathfrak{g}_1^d]^{G_0}$, which are of independent interest.
