  We review results on the Knizhnik-Zamolodchikov (KZ) and dynamical equations,
both differential and difference, in the context of the $(gl_k,gl_n)$ duality,
and their implications for hypergeometric integrals. The KZ and dynamical
equations naturally exchange under the duality, which provides two kinds of
integral formulae for hypergeometric solutions of the equations. This fact
yields identities for hypergeometric integrals of different dimensions, the
dimension of the first integral being the parameter of the second one, and vice
versa. Similar identites exist between hypergeometric and q-hypergeometric
integrals of Mellin-Barnes type of different dimensions. Those identites are
multidimensional analogues of the equality of two integral representations for
the Gauss hypergeometric function.
