有理曲面上的曲线与正交李代数的表示

本文研究了一类有理曲面上的有理曲线的configurations与Dn-型李代数的一个基本不可约表示(其最高权在正文中记作λ_(n-2))之间的关系,发现该不可约表示可以由对应的有理曲面上满足两组丢番图方程的(可约)有理曲线所给出,每组方程的解构成一个外尔群轨道.

Configurations of curves on rational surfaces and representations of orthogonal Lie algebras

We study the relation between certain rational surfaces and orthogonal Lie algebras (that is, $D_n$-Lie algebras). We find that a fundamental irreducible representation (whose highest weight is denoted by $\lambda_{n-2}$) is determined by finitely many rational curves on these surfaces satisfying two systems of Diophantine equations, and the solutions of each system of these equations form a Weyl group orbit.