I will discuss a generalized cluster on GL(n) compatible with the particular Poisson bracket that is homogeneous
w.r.t. two-sided action of a Poisson-Lie group G=GL(n)xGL(n). Here the components of G are equipped with two
„opposite” versions of the Cremmer-Gervais Poisson-Lie bracket. Our construction relies on birational Poisson maps
that relate the Poisson homogeneous structure under investigation with the phase space of the finite Toda lattice
and the Poisson dual of the Cremmer-Gervais Poisson-Lie group.
This is a joint work with M. Shapiro and A. Vainshtein.
(This is joint with the IRT seminar.)