Equalities and Inequalities on Products of Schur Functions

This lecture presents Daniel Soskin's research on "Equalities and Inequalities on Products of Schur Functions" at the Special Year Seminar II at the Institute for Advanced Study. Explore the ring of symmetric functions and Littlewood-Richardson coefficients as structure constants of Schur function bases. Learn about necessary conditions for Schur positivity of expressions like sλsμ−sρsν, building on work by Lam-Postnikov-Pylyavskyy who demonstrated Schur positivity of sλ∪μsλ∩μ−sλsμ and other inequalities conjectured by Okounkov and others. Discover new results based on Nguyen-Pylyavskyy's work on Temperley-Lieb immanants, including findings that cνλ∪μ,λ∩μ−cνλ,μ∈#P and equality conditions for previously proven inequalities. The presentation covers joint work in progress with Igor Pak and takes place on March 13, 2025, at 10:00am in Simonyi 101.