几何不变理论与广义本征值问题
Geometric Invariant Theory and Generalized Eigenvalue Problem
摘要：
设$H$是复连通约化群$G$的连通约化子群.固定$H$和$G$的极大环面和博雷尔子群。考虑$H$和$G$的不可约表示对$(V,V')$，使得$V$是$V'$的子模。我们感兴趣的锥$LR(G,H)$产生的对主导权这样一对表示。我们的主要结果给出了描述$LR(G,H)$作为主导腔的一部分的最小不等式集。通过这种方法，我们得到了关于Dolgachev-Hu的$G$ -样本锥的面和这个锥的变分的结果。
英文摘要：
Let $H$ be a connected reductive subgroup of a complex connected reductive group $G$. Fix maximal tori and Borel subgroups of $H$ and $G$. Consider the pairs $(V,V')$ of irreducible representations of $H$ and $G$ such that $V$ is a submodule of $V'$. We are interested in the cone $LR(G,H)$ generated by the pairs of dominant weights of such a pair of representations. Our main result gives a minimal set of inequalities describing $LR(G,H)$ as a part of the dominant chamber. In way, we obtain results about the faces of the Dolgachev-Hu's $G$-ample cone and variations of this cone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
