New classes of domains with explicit Bergman kernel
Complex Variables
2007-05-23 v2 Rings and Algebras
Abstract
We introduce two classes of "egg type" domains, built on general bounded symmetric domains, for which we compute the Bergmann kernel in explicit form. We use the characterization of bounded symmetric domains through Jordan triple systems. The egg type domains are defined using the generic norm. A generalization of the Hua integral is computed; the result shows the existence of a special polynomial with integer or half-integer coefficients, attached to each irreducible bounded symmetric domain.
Cite
@article{arxiv.math/0301322,
title = {New classes of domains with explicit Bergman kernel},
author = {Guy Roos and Weiping Yin},
journal= {arXiv preprint arXiv:math/0301322},
year = {2007}
}
Comments
22 pages. Version 2: presentation of the polynomial $\chi $ has been simplified and does no longer depend on the parity of $a$ and $r$. One reference precised