Acceptable Compact Lie Groups

Abstract

In this paper, we show that for a connected compact Lie group to be acceptable, it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups ${\text {SU}}(n)$, ${\text {Sp}}(n)$, ${\text {SO}}(2n+1)$, ${\text {G}}_2$, ${\text {SO}}(4)$. We show that there are invariant functions on ${\text {SO}}_{4}({\mathbb {C}})^{2}$ which are not generated by 1-argument invariants, though the group ${\text {SO}}_{4}({\mathbb {C}})$ is acceptable.

Funding

NSFC(11971036)