2011/09/21 by Patrick Desrosiers, Desrosiers, Patrick, Dang-Zheng Liu +1
Mathematics · Physics and Astronomy · #05E05 #15B52 #33C70 #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.MP #msc:05E05 #msc:15B52 #msc:33C70
paper · pdf · doi:10.48550/arxiv.1109.4659
43 pages
arxiv created 2011/09/21 · openalex publication_date 2011/09/21 · arxiv updated 2011/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a new Selberg-type integral with n+m indeterminates, which turns out to be related to the deformed Calogero-Sutherland systems. We show that the integral satisfies a holonomic system of n+m non-symmetric linear partial differential equations. We also prove that a particular hypergeometric function defined in terms of super Jack polynomials is the unique solution of the system. Some properties such as duality relations, integral formulas, Pfaff-Euler and Kummer transformations are also established. As a direct application, we evaluate the expectation value of ratios of characteristic polynomials in the classical β-ensembles of Random Matrix Theory.