A positivity conjecture for Jack polynomials

By Michel Lassalle. 2007

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We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for partitions having a rectangular shape.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

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