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New classes of domains with explicit Bergman kernel
Authors:Weiping?Yin  author-information"  >  author-information__contact u-icon-before"  >  mailto:wyin@mail.cnu.edu.cn"   title="  wyin@mail.cnu.edu.cn"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,Lu?Keping,Guy?Roos
Affiliation:1. Department of Mathematics, Capital Normal Univesity, Beijing 100037, China
2. Henan University, Kaifeng, 475001, China
3. Nevski Prospekt 113/4-53,191024 St Petersburg,Russian Federation
Abstract:We introduce two classes of egg type domains, built on general bounded sym-metric domains, for which we obtain the Bergman kernel in explicit formulas. As an aux-iliary tool, we compute the integral of complex powers of the generic norm on a boundedsymmetric domains using the well-known integral of Selberg. This generalizes matrix in-tegrals of Hua and leads to a special polynomial with integer or half-integer coefficientsattached to each irreducible bounded symmetric domain.
Keywords:Cartan domain  Bergman kernel  holomorphic automorphism group  bounded symmetric domain  Hua integral
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