Previous article Next article Sign Variations of the Macdonald IdentitiesDennis StantonDennis Stantonhttps://doi.org/10.1137/0517103PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractSign variations are given for the Macdonald identities for root systems of small rank. Limiting cases of these identities give properties of the eta function. Two such formulas are explicitly given.[1] Richard Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal., 11 (1980), 938–951 10.1137/0511084 82e:33002 0458.33002 LinkISIGoogle Scholar[2] F. Dyson, 1968, letter to L. Winquist, March Google Scholar[3] I. Macdonald, Affine root systems and Dedekind's $\eta$-function, Invent. Math., 15 (1972), 91–143 50:9996 0244.17005 CrossrefISIGoogle Scholar[4] I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal., 13 (1982), 988–1007 10.1137/0513070 84h:17006a 0498.17006 LinkISIGoogle Scholar[5] S. Milne, An elementary proof of the Macdonald identities for $A\sp {(1)}\sb l$, Adv. in Math., 57 (1985), 34–70 87e:17020 0586.33011 CrossrefISIGoogle Scholar[6] Lasse Winquist, An elementary proof of $p(11m+6)\equiv 0\,({\rm mod}\ 11)$, J. Combinatorial Theory, 6 (1969), 56–59 38:4434 0241.05006 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Leading coefficients of Morris type constant term identitiesAdvances in Applied Mathematics, Vol. 87 Cross Ref Logarithmic and Complex Constant Term Identities29 July 2013 Cross Ref A q-product Tutorial for a q-series Maple Package Cross Ref A New Proof of Winquist's IdentityJournal of Combinatorial Theory, Series A, Vol. 78, No. 2 Cross Ref Macdonald’s constant term conjectures for exceptional root systems1 January 1991 | Bulletin of the American Mathematical Society, Vol. 24, No. 2 Cross Ref A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q-Morris identityDiscrete Mathematics, Vol. 79, No. 3 Cross Ref The crank of partitions mod 8,9 and 101 January 1990 | Transactions of the American Mathematical Society, Vol. 322, No. 1 Cross Ref An Elementary Approach to the Macdonald Identities Cross Ref A Unified Approach to Macdonald’s Root-System ConjecturesDoron Zeilberger17 July 2006 | SIAM Journal on Mathematical Analysis, Vol. 19, No. 4AbstractPDF (2886 KB)First layer formulas for characters of 𝑆𝐿(𝑛,𝐶)1 January 1987 | Transactions of the American Mathematical Society, Vol. 299, No. 1 Cross Ref Volume 17, Issue 6| 1986SIAM Journal on Mathematical Analysis History Submitted:17 December 1984Accepted:16 September 1985Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0517103Article page range:pp. 1454-1460ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics