# Seminar talk, 16 December 2015

Title: Decompositions of the group ${\displaystyle G(2)}$ and related integrable hierarchies
The group ${\displaystyle G(2)}$ of all invertible transformations of a Hilbert space that differ from the identity an operator of the Hilbert-Schmidt class, played a role in the work of Shale on symmetries for free boson fields. In this talk we explain the role various decompositions of this group plays in the construction of solutions of various integrable hierarchies, both of KdV- and of Toda-type.