Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. II
The Toda lattice hierarchy is shown to have the virtual Bruhat decomposition of the \(A_ \infty\) group as its parameter space, instead of the Grassmann manifold for the KP hierarchy. The open cell of this Bruhat decomposition was examined in the first part of this series [Lett. Math. Phys. 21, No. 1, 77-84 (1991; Zbl 0733.35098)]. In the present paper, based on the above work, a one-to-one correspondence between points in the small cells and pseudo-regular solutions is established.
scientific article; zbMATH DE number 55945