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Keywords:
Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group
Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group
Summary:
We prove that there are at least two new non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics on ${\rm Sp} (l+3k)$ $(k < l)$. It implies that every compact simple Lie group ${\rm Sp} (n)$ for $n= l+3k>4$ admits at least $2[\tfrac 14 (n-1)]$ non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics.
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