\(\text{SL}(2)\) and \(z\)-measures (Q2759655)

\(z\)-measures are defined to be a two-parameter family of measures on partitions introduced in the context of harmonic analysis of the infinite symmetric group. Kerov constructed an \(SL(2)\)-action on partitions for which \(z\)-measures are certain matrix elements. Borodin and Olshanski computed the correlation functions of \(z\)-measures in terms of the hypergeometric function appearing in the matrix elements of the representations of \(SL(2)\). This paper gives a representation-theoretic derivation of the determinantal formula of Borodin and Olshanski for the correlation functions of \(z\)-measures in terms of the hypergeometric kernel.NEWLINENEWLINEFor the entire collection see [Zbl 0967.00059].