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arXiv · 1403.8139

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

Vineet Gupta·Uma Roy·Roger Van Peski
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Abstract

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 polynomial. 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.

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Vineet Gupta, Uma Roy, Roger Van Peski. 2014-09-24. A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials. https://arxiv.org/abs/1403.8139

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