摘要
We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of the generic norm on a bounded symmetricdomains using the well-known integral of Selberg. Thisgeneralizes matrix integrals of Hua and leads to a specialpolynomial with integer or half-integer coefficients attached toeach irreducible bounded symmetric domain.
We introduce two classes of egg type domains, built on general bounded symmetric domains, for which we obtain the Bergman kernel in explicit formulas. As an auxiliary tool, we compute the integral of complex powers of the generic norm on a bounded symmetric domains using the well-known integral of Selberg. This generalizes matrix integrals of Hua and leads to a special polynomial with integer or half-integer coefficients attached to each irreducible bounded symmetric domain.
