Macdonald-positive specializations of the algebra of symmetric functions: proof of the Kerov conjecture (Q1711494)

This article proves a conjecture stated by \textit{S. V. Kerov} [in: Representation theory and dynamical systems. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. 67--94 (1992; Zbl 0760.05089)], which describes the classification of homomorphisms from the algebra of symmetric functions to \(\mathbb{R}\) with nonnegative values on Macdonald symmetric functions. As a common procedure in the field, the proof is done in two steps. In this case, these two steps are pole removal and diffusivity argument.