New classes of domains with explicit Bergman kernel

作     者：Roos GUY 

作者机构：Henan University Kaifeng 475001 China Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2004年第47卷第3期

页      面：352-371页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Cartan domain, Bergman kernel, holomorphic automorphism group, boundedsymmetric domain, Hua integral. 

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.