论文标题
正交组的本地Plücker公式
Local Plücker formulas for orthogonal groups
论文作者
论文摘要
局部plücker公式将图像曲线的指标向量与相关曲线的plücker嵌入在探测空间中的全体形态曲线上，与相应的曲面矢量相关。 Givental指出，曲线的向量是根据指标向量通过$ a_n $的Cartan矩阵表示的，并将此观察结果从类型的$ a_n $扩展到所有非感受类型。在本文中，我们展示了特殊正交组的本地plücker公式，即可以通过简化为经典的$ a_n $ case来获得$ b_n $和$ d_n $的cartan矩阵。
Local Plücker formulas relate the vector of metrics on a holomorphic curve in the projective space, induced by the Fubini-Study metrics on projetive spaces via Plücker embeddings of associated curves, to the corresponding vector of curvatures. Givental noted that the vector of curvatures is expressed in terms of the vector of metrics via Cartan matrix of type $ A_n$ and extended this observation from type $A_n$ to all nonexceptional types. In this paper we show how local Plücker formulas for special orthogonal groups, i.e. for Cartan matrices of type $ B_n$ and $ D_n$, can be obtained by reduction to the classical $A_n$ case.
