As an auxiliary tool, we compute the integral of complex powers of the generic norm on a bounded symmetric domains, using the well-known integral of Selberg. This generalizes matrix integrals of L. K. Hua. The result leads to a special polynomial with integer or half-integer coefficients, attached to each irreducible bounded symmetric domain.
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(This paper has been published in Science in China Ser. A Mathematics 47 (3) (2004), 352-371 (English version) and Science in China Ser. A Mathematics 34 (3) (2004), 283-303 (Chinese version). The authors are YIN Weiping, LU Keping and ROOS Guy.)
Guy Roos < guy.roos@laposte.net >
Weiping Yin < wyin@mail.cnu.edu.cn >