Commuting Toeplitz operators and moment maps on Cartan domains of type III

David Cuevas-Estrada, Raul Quiroga-Barranco

Let $D_n^{III}$ and ${\mathcal{S}}_n$ be the Cartan domains of type III that consist of the symmetric $n\times n$ complex matrices $Z$ that satisfy $Z\overline{Z}<I_n$ and $\mathr…