On the evaluation of some Selberg-like integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article

Binegar, B.

关键词: Selberg integral;    symmetric functions;    associated variety;   

DOI  :  10.1016/j.jmaa.2008.01.040

来源: Elsevier

【 摘 要 】

Several methods of evaluation are presented for a family {I-n,I-d,I-p} of Selberg-like integrals that arise in the computation of the algebraic-geometric degrees of a family of spherical nilpotent orbits associated to the symmetric space of a simple real Lie group. Adapting the technique of Nishiyama, Ochiai and Zhu, we present an explicit evaluation in terms of certain iterated sums over permutation groups. The resulting formula, however, is only valid when the integrand involves an even power of the Vandermonde determinant. We then apply, to the general case, the theory of symmetric functions and obtain an evaluation of the integral I-n,I-d,I-p as a product of polynomial of fixed degree times a particular product of gamma factors; thereby identifying the asymptotics of the integrals with respect to their parameters. Lastly, we derive a recursive formula for evaluation of another general class of Selberg-like integrals, by applying some of the technology of generalized hypergeometric functions. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free