Symplectic and Kähler structures on biquotients

Abstract

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 $\mathrm{SU}(4)//T^3$.

v2: added references and Theorem 3.3. Comments are welcome!