  I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying
pairs (A,B) of commuting nilpotent operators on a vector space contains the
problem of classifying an arbitrary t-tuple of linear operators. Moreover, it
contains the problem of classifying representations of an arbitrary quiver, and
so it is considered as hopeless. We give a simple normal form of the matrices
of (A,B) if the intersection of kernels of A and B is one-dimensional. We prove
that this form is canonical if the Jordan matrix of A is a direct sum of Jordan
blocks of the same size and the field is of zero characteristic.
