2014/03/31 by Vineet Gupta, Gupta, Vineet, Uma Roy +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1403.8139
openalex publication_date 2014/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theorem due to Tokuyama expresses Schur polynomials in terms of\nGelfand-Tsetlin patterns, providing a deformation of the Weyl character formula\nand two other classical results, Stanley's formula for the Schur\nq-polynomials and Gelfand's parametrization for the Schur polynomial. We\ngeneralize Tokuyama's formula to the Hall-Littlewood polynomials by extending\nTokuyama's statistics. Our result, in addition to specializing to Tokuyama's\nresult and the aforementioned classical results, also yields connections to the\nmonomial symmetric function and a new deformation of Stanley's formula.\n