Haglund-haiman-loehr Type Formulas for Hall-littlewood Polynomials of Type B and C

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 HaglundHaiman-Loehr formula for Macdonald polynomials. The second is the type A instance of Schwer’s formula (rephrased and rederived by Ram) for HallLittlewood 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.