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New Einstein metrics on Sp ( n ) which are non-naturally reductive

Shaoxiang ZhangHuibin Chen — 2022

Czechoslovak Mathematical Journal

We prove that there are at least two new non-naturally reductive Ad ( Sp ( l ) × Sp ( k ) × Sp ( k ) × Sp ( k ) ) invariant Einstein metrics on Sp ( l + 3 k ) ( k < l ) . It implies that every compact simple Lie group Sp ( n ) for n = l + 3 k > 4 admits at least 2 [ 1 4 ( n - 1 ) ] non-naturally reductive Ad ( Sp ( l ) × Sp ( k ) × Sp ( k ) × Sp ( k ) ) invariant Einstein metrics.

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