  We describe U(N)-monopoles (N > 1) on Kerr black holes by the parameters of
the moduli space of holomorphic vector U(N)-bundles over two-sphere with the
help of the Grothendieck splitting theorem. For N = 2,3 we obtain this
description in an explicit form as well as the estimates for the corresponding
monopole masses. This gives a possibility to adduce some reasonings in favour
of existence of both a fine structure for Kerr black holes and the statistical
ensemble tied with it which might generate the Kerr black hole entropy.
