University of Sydney Algebra Seminar

Yusra Naqvi (University of Sydney)

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

Symmetries in binomial coefficients for Jack polynomials

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.