Some new results on dimension datum

نویسندگان

چکیده

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 $SU(4n+2)$, find a family pairs irreducible representations $(\tau_1,\tau_2)\in\hat{H_{1}}\times\hat{H_{2}}$ such that $\mathscr{D}_{H_1,\tau_1}=\mathscr{D}_{H_2,\tau_2}$. With construct examples isospectral hermitian vector bundles. Secondly, that: $\tau$-dimension data one-dimensional connected compact Lie group $H$ determine the image homomorphism from to given $G$. Lastly, improve compactness result an set normal homogeneous spaces $(G/H,m)$ by allowing Riemannian metric $m$ vary, but posing constraint $G$ is semisimple.

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ژورنال

عنوان ژورنال: Bulletin of The London Mathematical Society

سال: 2022

ISSN: ['1469-2120', '0024-6093']

DOI: https://doi.org/10.1112/blms.12605