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Algebra and Combinatorics Seminar: Apoorva Khare, Indian Institute of Science (Bangalore, India), Schur polynomials: from smooth functions to symmetric function identities
Algebra and Combinatorics Seminar: Apoorva Khare, Indian Institute of Science (Bangalore, India), Schur polynomials: from smooth functions to symmetric function identities
Cauchy's determinantal identity (1840s) expands via Schur polynomials the determinant of the matrix f, where f(t) = 1/(1-t) is applied entrywise to the rank-one matrix u v^T = (u_i v_j). This theme has resurfaced in the 2010s in analysis (following a 1960s computation by Loewner), in the quest to find polynomials p(t) with a negative coefficient that entrywise preserve…