An analytic framework for the two-dimensional infinite Toda hierarchy associated with a commutative algebra (Q1002615)

The authors construct a solution to the two-dimensional infinite Toda hierarchy associated to a maximal commutative subalgebra of the algebra of complex \(k\times k\)-matrices. The solution is obtained with the help of the group of (invertible) operators on the Hilbert space \(L^2(S^1,\mathbb{C}^k)\) that differ from identity by a trace class operator, and is given in terms of \(\mathbb{Z}\times \mathbb{Z}\)-matrices.