Generalized cluster structures related to Poisson duals of ${\mathrm{SL}}_n$

Michael Gekhtman, Dmitriy Voloshyn

We study Poisson varieties $({\mathrm{SL}}_n,{\pi }_{\bar{\mathbf{\Gamma }}}^{†})$ parameterized by Belavin--Drinfeld quadruples $\bar{\mathbf{\Gamma }}:=(\mathbf{\Gamma },r_0)$ of type $A_{n-1}$ along wit…