Departmental Seminar

From exactly solvable lattice models to symmetric functions: two examples

Professor Paul Zinn-Justin
UniversitĀ“e Pierre et Marie Curie Paris 6 (France)

We'll discuss an approach to studying certain families of symmetric polynomials which is based on exactly solvable two-dimensional lattice models. After explaining the general strategy on the classical case of Schur polynomials/functions, we'll provide two more advanced examples: Hall--Littlewood polynomials and Grothendieck polynomials. As an application, we shall describe new Cauchy-type identities for the former (as well as their type BC counterparts), and variations on the Littlewood--Richardson rule for the latter.

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