Galilean symmetry of the KdV hierarchy

By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non-abelian Born–Infeld partition function and the generalized Brézin–Gross–Witten partition function.