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Lie Group Quantum Mathematics Seminar

Positivity of interpolation polynomials

Emily Sergel, Rutgers University

Location:  zoom
Date & time: Friday, 12 February 2021 at 12:00PM - 1:00PM

Abstract: The interpolation polynomials are a  family of
inhomogeneous symmetric polynomials characterized
by simple vanishing properties. In 1996, Knop and Sahi
showed that their top homogeneous components are
Jack polynomials. For this reason these polynomials are
sometimes called interpolation Jack polynomials, shifted
Jack polynomials, or Knop-Sahi polynomials.

We prove Knop and Sahi's main conjecture from 1996,
which asserts that, after a suitable normalization, the
interpolation polynomials have positive integral coefficients.
This result generalizes Macdonald's conjecture for Jack
polynomials that was proved by Knop and Sahi in 1997.
Moreover, we give a combinatorial expansion for the
interpolation polynomials that exhibits the desired
positivity property.

This is joint work with Y. Naqvi and S. Sahi.

Zoom link:
Meeting ID: 939 2146 5287
Passcode: 196884

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