Acceptable Compact Lie Groups
Jun Yu
Peking Mathematical Journal ›› 2021, Vol. 5 ›› Issue (2) : 427 -446.
Acceptable Compact Lie Groups
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.
NSFC(11971036)
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