Vol. 4, No. 7, 2010

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11
Issue 10, 2213–2445
Issue 9, 1967–2212
Issue 8, 1739–1965
Issue 7, 1489–1738
Issue 6, 1243–1488
Issue 5, 1009–1241
Issue 4, 767–1007
Issue 3, 505–765
Issue 2, 253–503
Issue 1, 1–252

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Haglund–Haiman–Loehr type formulas for Hall–Littlewood polynomials of type $B$ and $C$

Cristian Lenart

Vol. 4 (2010), No. 7, 887–917

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.

Hall–Littlewood polynomials, Macdonald polynomials, alcove walks, Schwer's formula, the Haglund–Haiman–Loehr formula
Mathematical Subject Classification 2000
Primary: 05E05
Secondary: 33D52
Received: 16 July 2009
Revised: 11 July 2010
Accepted: 13 October 2010
Published: 29 January 2011
Cristian Lenart
Department of Mathematics and Statistics
State University of New York at Albany
1400 Washington Avenue
Albany, NY 12222
United States