  We obtain a family of matrix integrals which decompose to a product of
Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but
generally speaking essentially differ from it).
  We obtain Plancherel formula for Berezin representations for all series of
classical groups (for large values of parameters of representations).
  The Berezin representations are deformations of L^2 on Riemann noncompact
symmetric spaces G/K defined by Berezin kernels, i.e powers of |det(1-zu^*)|
(in matrix ball models). These representations also can be obtained by
restrictions of holomorphic representations of some group Q containing G as
symmetric subgroup.
  We also discuss models of noncompact Riemann symmetric spaces: matrix balls,
matrix cones, matrix wedges, and sections of wedges.
