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arxiv: 1711.06939 · v2 · submitted 2017-11-18 · 🧮 math.RT · math.CO

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

Konstantin Matveev
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classification 🧮 math.RT math.CO
keywords functionssymmetricalgebrakerovclassificationconjectureconjecturedhomomorphisms
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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.

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    Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probabi...