A combinatorial conjecture related with complex bounded symmetric domains
The Hua integral, i.e. the integral of the power $s$ of the generic
norm on a bounded circled symmetric domain, is the inverse $1 / \chi(s)$ of a
polynomial $\chi$ which can be expressed via the usual inariants $a$, $b$, $r$
of the associated Jordan triple. We state a conjecture about the sign of the
coefficients of the expansion of $\chi(\mu s)$ in raising factorials of
$s+1$. The conjecture has been checked with help of computer algebra software
in many significant cases. If the conjecture is true, it would allow to
compare the Bergman metric of some Hartogs domains built over bounded
symmetric domains, with the Kaehler-Einstein metric of the same domains.
Guy Roos < guy.roos@normalesup.org >