论文标题
维度基准的一些新结果
Some new results on dimension datum
论文作者
论文摘要
在本文中，我们展示了有关维度基准的三个新结果。首先，对于两个子组，$ h_ {1} $（$ \ cong u（2n+1）$）和$ h_ {2} $（$ \ cong sp（n）\ times so（2n+2）$（4n+2）$ $（τ_1，τ_2）\ in \ hat {h_ {1}} \ times \ hat {h_ {2}} $，这样，$ \ mathscr {d} _ {h_1，τ_1，τ_1} = \ mathscr {d} _ {d} _ {h_2} _ {通过此，我们构建了同一偏僻的遗传学矢量束的例子。其次，我们表明：$τ$ - 二维数据的一维紧凑型谎言组$ h $的一维表示，确定同构的图像从$ h $到给定的紧凑型谎言组$ g $。最后，我们通过允许Riemannian Metric $ m $变化来改善一套正常均匀空间$（g/h，m）$的紧凑性结果，但对$ g $是半imimple的约束。
In this paper we show three new results concerning dimension datum. Firstly, for two subgroups $H_{1}$($\cong U(2n+1)$) and $H_{2}$($\cong Sp(n)\times SO(2n+2)$) of $SU(4n+2)$, we find a family of pairs of irreducible representations $(τ_1,τ_2)\in\hat{H_{1}}\times\hat{H_{2}}$ such that $\mathscr{D}_{H_1,τ_1}=\mathscr{D}_{H_2,τ_2}$. With this we construct examples of isospectral hermitian vector bundles. Secondly, we show that: $τ$-dimension data of one-dimensional representations of a connected compact Lie group $H$ determine the image of homomorphism from $H$ to a given compact Lie group $G$. Lastly, we improve a compactness result for an isospectral set of normal homogeneous spaces $(G/H,m)$ by allowing the Riemannian metric $m$ vary, but posing a constraint that $G$ is semisimple.
