Abstract
In previous work we showed that two apparently unrelated formulas for the Hall–Littlewood polynomials of type are, in fact, closely related. The first is the tableau formula obtained by specializing in the Haglund–Haiman–Loehr formula for Macdonald polynomials. The second is the type 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 and 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 new tableau formulas for the Hall–Littlewood polynomials of type and by compressing the corresponding instances of Schwer’s formula.
Citation
Cristian Lenart. "Haglund–Haiman–Loehr type formulas for Hall–Littlewood polynomials of type $B$ and $C$." Algebra Number Theory 4 (7) 887 - 917, 2010. https://doi.org/10.2140/ant.2010.4.887
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