Symplectic and Kähler structures on biquotients

We construct symplectic structures on roughly half of all equal rank biquotients of the form $G //T$, where $G$ is a compact simple Lie group and $T$ a torus, and investigate Hamiltonian Lie group actions on them. For the Eschenburg flag, this action has similar properties as Tolman’s and Woodward’s examples of Hamiltonian non-Kähler actions. In addition to the previously known Kähler structure on the Eschenburg flag, we find another Kähler structure on a biquotient $\operatorname{SU}(4) // T^3$.

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Received 8 May 2019

Accepted 16 July 2019

Published 30 July 2020