A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials
A Generalization of Tokuyama's Formula to the Hall-Littlewood Polynomials
复制标题
德山公式对 Hall-Littlewood 多项式的推广
DOI：
10.37236/4732
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发表时间：
2014
影响因子：
0.7
通讯作者：
Roger Van Peski
中科院分区：
文献类型：
--
作者：
Vineet Gupta;Uma Roy;Roger Van Peski
Tokuyama的一个定理用Gelfand-Tsetlin模式表示Schur多项式，给出了Weyl特征标公式和另外两个经典结果的变形，即关于Schur$q$-多项式的Stanley公式和关于Schur多项式的Gelfand的参数化。通过推广德山的统计量，我们将德山公式推广到Hall-Littlewood多项式。我们的结果，除了特化了德山的结果和前述的经典结果外，还给出了与单项对称函数和Stanley公式的新变形的联系。
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.