Geodesic
A generalization of Tokuyama's formula to the Hall-Littlewood polynomials
Vineet Gupta1 ; Uma Roy2 ; Roger Van Peski3
1Stanford University
2PROMYS
3Princeton University
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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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.
DOI : 10.37236/4732
Classification : 05E05
Mots-clés : Hall-Littlewood polynomials, Tokuyama's formula, Gelfand-Tsetlin patterns

Vineet Gupta  1   ; Uma Roy  2   ; Roger Van Peski  3

1 Stanford University
2 PROMYS
3 Princeton University 
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     author = {Vineet Gupta and Uma Roy and Roger Van Peski},
     title = {A generalization of {Tokuyama's} formula to the {Hall-Littlewood} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {2},
     doi = {10.37236/4732},
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Vineet Gupta; Uma Roy; Roger Van Peski. A generalization of Tokuyama's formula to the Hall-Littlewood polynomials. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4732

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