zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Lie algebraic approaches to classical partition identities. (English) Zbl 0384.10008

11P81Elementary theory of partitions
17B65Infinite-dimensional Lie (super)algebras
05A17Partitions of integers (combinatorics)
Full Text: DOI
[1] Andrews, G. E.: A general theory of identities of the Rogers-Ramanujan type. Bull. amer. Math. soc. 80, 1033-1052 (1974) · Zbl 0301.10016
[2] Andrews, G. E.: The theory of partitions. Encyclopeadia of mathematics and its applications 2 (1976)
[3] D. M. Bressoud, A functional generalization of the Rogers-Ramanujan identities with interpretation, J. Combinatorial Theory, Ser. A, to appear. · Zbl 0414.10004
[4] Carlitz, L.; Subbarao, M. V.: A simple proof of the quintuple product identity. Proc. amer. Math. soc. 32, 42-44 (1972) · Zbl 0234.05005
[5] Cheema, M. S.: Vector partitions and combinatorial identities. Math. comp. 18, 414-420 (1964) · Zbl 0196.29002
[6] Connor, W. G.: Partition theorems related to some identities of Rogers and Watson. Trans. amer. Math. soc. 214, 95-111 (1975) · Zbl 0313.10012
[7] Dyson, F. J.: Missed opportunities. Bull. amer. Math. soc. 78, 635-653 (1972) · Zbl 0271.01005
[8] A. Feingold and J. Lepowsky, The Weyl-Kac character formula and power series identities, to appear. · Zbl 0391.17009
[9] Franklin, F.: Sur le développement du produit infini (1 - x)(1 - x2)(1 - x3) $\dots $. CR acad. Sci. Paris 82, 448-450 (1881) · Zbl 13.0188.01
[10] Garland, H.; Lepowsky, J.: Lie algebra homology and the macdonald-Kac formulas. Invent. math. 34, 37-76 (1976) · Zbl 0358.17015
[11] Humphreys, J. E.: Introduction to Lie algebras and representation theory. (1972) · Zbl 0254.17004
[12] . Math. USSR-izv. A 2, 1271-1311 (1968)
[13] . Functional analysis and its applications 8, 68-70 (1974)
[14] Lepowsky, J.: Macdonald-type identities. Advances in math. 27, 230-234 (1978) · Zbl 0388.17003
[15] Generalized Verma modules, loop space cohomology and Macdonald-type identities, to appear. · Zbl 0414.17007
[16] Application of the numerator formula to k-rowed plane partitions, to appear. · Zbl 0425.10015
[17] J. Lepowsky and R. L. Wilson, Construction of the affine Lie algebra, A(1)1, to appear. · Zbl 0388.17006
[18] Macdonald, I. G.: Affine root systems and Dedekind’s ${\eta}$-function. Invent. math. 15, 91-143 (1972) · Zbl 0244.17005
[19] S. Milne, A direct combinatorial proof of the quintuple product identity, to appear.
[20] S. Milne and R. L. Wilson, Jacobi’s triple-product identity from elementary homology computations, to appear.
[21] Moody, R. V.: A new class of Lie algebras. J. algebra 10, 211-230 (1968) · Zbl 0191.03005
[22] Moody, R. V.: Macdonald identities and Euclidean Lie algebras. Proc. amer. Math. soc. 48, 43-52 (1975) · Zbl 0315.17003
[23] Slater, L. J.: Further identities of the Rogers-Ramanujan type. Proc. London math. Soc. 54, No. 2, 147-167 (1952) · Zbl 0046.27204
[24] Zolnowsky, J.: A direct combinatorial proof of the Jacobi identity. Discrete math. 9, 293-298 (1974) · Zbl 0292.10014