Algebra Seminar: Naqvi -- Symmetries in binomial coefficients for Jack polynomials

Yusra Naqvi (University of Sydney) 

Friday 19 October, 12-1pm, Place: Carslaw 375 

Title: Symmetries in binomial coefficients for Jack polynomials 

Abstract: Jack polynomials generalise several classical families of symmetric
polynomials, including Schur polynomials.  Generalised binomial coefficients for Jack
polynomials are as complicated as the Jack polynomials themselves, and there is an
ongoing search for more direct combinatorial formulas for these coefficients.  In this
talk, I will describe these coefficients and their connections with
Littlewood-Richardson coefficients and Jack interpolation polynomials.  I will also
discuss some direct formulas in special cases that reveal unexpected symmetries in these
coefficients.  This talk is based on joint work with Siddhartha Sahi and Emily Sergel.