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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

An A$_2$ Bailey lemma
and Rogers-Ramanujan-type identities


Authors: George E. Andrews, Anne Schilling and S. Ole Warnaar
Journal: J. Amer. Math. Soc. 12 (1999), 677-702
MSC (1991): Primary 05A30, 05A19; Secondary 33D90, 33D15, 11P82
Published electronically: April 23, 1999
MathSciNet review: 1669957
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Abstract | References | Similar Articles | Additional Information

Abstract: Using new $q$-functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A$_2$ version of the classical Bailey lemma. We apply our result, which is distinct from the A$_2$ Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W$_3$ algebra.


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Additional Information

George E. Andrews
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: andrews@math.psu.edu

Anne Schilling
Affiliation: Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
Email: schillin@wins.uva.nl

S. Ole Warnaar
Email: warnaar@wins.uva.nl

DOI: http://dx.doi.org/10.1090/S0894-0347-99-00297-0
PII: S 0894-0347(99)00297-0
Keywords: A$_2$ Bailey lemma, Rogers--Ramanujan identities
Received by editor(s): August 8, 1998
Published electronically: April 23, 1999
Additional Notes: The second author was supported by the “Stichting Fundamenteel Onderzoek der Materie”.
The third author was supported by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
Article copyright: © Copyright 1999 American Mathematical Society