Macdonald-positive specializations of the algebra of symmetric functions: Proof of the Kerov conjecture

TL;DR

This paper proves Kerov's 1992 conjecture by classifying all algebra homomorphisms from symmetric functions to real numbers that are non-negative on Macdonald functions, advancing understanding of symmetric function specializations.

Contribution

It provides a complete proof of Kerov's conjecture, offering a definitive classification of Macdonald-positive specializations of symmetric functions.

Findings

Classification of Macdonald-positive specializations established

Confirmed conjecture by S.V. Kerov from 1992

Enhanced understanding of symmetric function algebra structure

Abstract

We prove the classification of homomorphisms from the algebra of symmetric functions to $\mathbb{R}$ with non-negative values on Macdonald symmetric functions $P_{\lambda}$, that was conjectured by S.V. Kerov in 1992.