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2010 Haglund–Haiman–Loehr type formulas for Hall–Littlewood polynomials of type $B$ and $C$
Cristian Lenart
Algebra Number Theory 4(7): 887-917 (2010). DOI: 10.2140/ant.2010.4.887


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 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 B and C by compressing the corresponding instances of Schwer’s formula.


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Cristian Lenart. "Haglund–Haiman–Loehr type formulas for Hall–Littlewood polynomials of type $B$ and $C$." Algebra Number Theory 4 (7) 887 - 917, 2010.


Received: 16 July 2009; Revised: 11 July 2010; Accepted: 13 October 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1229.05274
MathSciNet: MR2776877
Digital Object Identifier: 10.2140/ant.2010.4.887

Primary: 05E05
Secondary: 33D52

Keywords: alcove walks , Hall–Littlewood polynomials , Macdonald polynomials , Schwer's formula , the Haglund–Haiman–Loehr formula

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.4 • No. 7 • 2010
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