2009/04/16 by Cristian Lenart, Lenart, Cristian
Mathematics · #05E05 #33D52 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E05 #msc:33D52
paper · pdf · doi:10.48550/arxiv.0904.2407
arxiv created 2009/04/16 · openalex publication_date 2009/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In previous work we showed that two apparently unrelated formulas for the Hall-Littlewood polynomials of type A are, in fact, closely related. The first is the tableau formula obtained by specializing q=0 in the Haglund-Haiman-Loehr formula for Macdonald polynomials. The second is the type A instance of Schwer's formula (rephrased and rederived by Ram) for Hall-Littlewood polynomials of arbitrary finite type; Schwer's formula is in terms of so-called alcove walks, which originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. We showed that the tableau formula follows by "compressing" Ram's version of Schwer's formula. In this paper, we derive tableau formulas for the Hall-Littlewood polynomials of type B and C by compressing the corresponding instances of Schwer's formula.