2006/08/12 by B. Binegar, Binegar, B.
Mathematics · #05E05 #32M15 #33D70 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E05 #msc:32M15 #msc:33D70
paper · pdf · doi:10.48550/arxiv.math/0608301
typos corrected
openalex publication_date 2006/08/12 · arxiv created 2006/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several methods of evaluation are presented for a family of Selberg-like integrals that arose in the computation of the algebraic-geometric degrees of a family of multiplicity-free nilpotent KC-orbits. First, adapting the technique of Nishiyama, Ochiai and Zhu, we present an explicit evaluation in terms of certain iterated sums over permutations groups. Secondly, using the theory of symmetric functions we obtain an evaluation 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.