New classes of domains with explicit Bergman kernel

2003/01/31 by Guy Roos, Weiping Yin
Mathematics · #math.CV #math.RA #msc:32A #msc:32M #msc:17C

paper · pdf

published as Science in China Ser.A Mathematics 2004 vol.47(3) 352-371 (English version) - Science in China Ser.A Mathematics 2004, 34(3), 283-303 (Chinese version) · 22 pages. Version 2: presentation of the polynomial $χ$ has been simplified and does no longer depend on the parity of $a$ and $r$. One reference precised

arxiv created 2003/03/31 · arxiv updated 2009/11/30

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.

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