Abstract
be a matrix of complex numbers, z* its conjugate transpose and I the identity matrix. Let D be the domain E [z | I-zz* >0]. The set B=E[zlzz*=I] forms a proper part of the boundary of D. Hua [3; 4] has shown by means of representation theory that there exists an orthonormal system (ONS) of homogeneous polynomials in D with respect to the inner product fDfgd VD. In this paper we exhibit such a system {I O} explicitly on D in a special case, only with respect to the inner product
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