A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials

  • Vineet Gupta
  • Uma Roy
  • Roger Van Peski
Keywords: Hall-Littlewood polynomials, Tokuyama’s formula, Gelfand-Tsetlin patterns


A theorem due to Tokuyama expresses Schur polynomials in terms of Gelfand-Tsetlin patterns, providing a deformation of the Weyl character formula and two other classical results, Stanley's formula for the Schur $q$-polynomials and Gelfand's parametrization for the Schur polynomials. We generalize Tokuyama's formula to the Hall-Littlewood polynomials by extending Tokuyama's statistics. Our result, in addition to specializing to Tokuyama's result and the aforementioned classical results, also yields connections to the monomial symmetric function and a new deformation of Stanley's formula.

Author Biographies

Vineet Gupta, Stanford University
Undergraduate, Department of Mathematics
Roger Van Peski, Princeton University
Undergraduate, Department of Mathematics
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