Dimensions of the Rings of Invariant Differential Operators on Bounded Homogeneous Domains

  • Hung-Hsi Wu
Part of the The University Series in Mathematics book series (USMA)


Let D be a bounded homogeneous domain in ℂ n , and suppose G(D) is the identity component of the analytic automorphism group of D. By a famous theorem of H. Cartan, G(D) is a real Lie group. We might as well assume that 0 ∈ D. From a well-known result in function theory of several complex variables the isotropy group G o (D) of G(D) at 0 ∈ D has the following representation:
$$\omega =zA+o(z),$$
where , \(z=\left( {{z}_{1}},\ldots ,{{z}_{r}} \right),\omega =\left( {{\omega }_{1}}\ldots ,{{\omega }_{n}} \right),\),and A is an n × n complex matrix constituting the linear parts {A}of G o (D), which form a compact subgroup of the unitary group U(n) denoted by K.


Irreducible Representation Compact Subgroup Homogeneous Part Classical Domain Irreducible Decomposition 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Hung-Hsi Wu
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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