References
Andrews, G.E.: The theory of partitions. Encyclopedia of Mathematics and its Applications, Vol. 2, Rota, G.-C. (ed.). Reading: Addison-Wesley 1976
Date, E. Jimbo, M., Kashiwara, M., Miwa, T.: Transformation groups for soliton equations-Euclidean Lie algebras and reduction of the KP hierarchy. Publ. Res. Inst. Math. Sci. Kyoto University18, 1077–1110 (1982)
Date, E., Kashiwara, M., Miwa, T.: Vertex operators and τ functions-transformation groups for solution equations II. Proc. Japan Acad. Sci. A Math. Sci.57, 387–392 (1981)
Feingold, A., Lepowsky, J.: The Weyl-Kac character formula and power series identities. Advances in Math.29, 271–309 (1978)
Frenkel, I.B.: Representations of affine Lie algebras, Hecke modular forms and Korteweg-deVries type equations, Proc. 1981 Rutgers Conference on Lie Algebras and Related Topics. Lecture Notes in Mathematics, vol. 933 pp. 71–110. Berlin-Heidelberg-New York: Springer 1982
Frenkel, I.B., Kac, V.G.: Basic representations of affine Lie algebras and dual resonance models. Invent. Math.62, 23–66 (1980)
Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976)
Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York: Academic Press 1978
Kac, V.G.: Simple irreducible graded Lie algebras of finite growth. Izv. Akad. Nauk SSSR32, 1323–1367 (1968); (English transl., Math. USSR Izv.2, 1271–1311 (1968)
Kac, V.G.: Automorphisms of finite order of semisimple Lie algebras. Funkcional. Anal. i Priložen.3, 94–96 (1969); (English transl., Functional Anal. Appl.3, 252–254 (1969)
Kac, V.G.: Infinite-dimensional Lie algebras and Dedekind's η-function. Funkcional. Anal. i Priložen.8, 77–78 (1974); (English transl., Functional Anal. Appl.8, 68–70 (1974)
Kac, V.G.: Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula. Advances in Math.30, 85–136 (1978)
Kac, V.G., Kazhdan, D.A., Lepowsky, J., Wilson, R.L.: Realization of the basic representations of the Euclidean Lie algebras. Advances in Math.42, 83–112 (1981)
Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math.81, 973–1032 (1959)
Lepowsky, J.: Macdonald-type identities. Advances in Math.27, 230–234 (1978)
Lepowsky, J.: Lectures on Kac-Moody Lie algebras. Université Paris VI, spring, 1978
Lepowsky, J.: Generalized Verma modules, loop space cohomology and Macdonald-type identities. Ann. Sci. École Norm. Sup.12, 169–234 (1979)
Lepowsky, J.: Application of the numerator formula tok-rowed plane partitions. Advances in Math.35, 179–194 (1980)
Lepowsky, J.: Affine Lie algebras and combinatorial identities. Proc. 1981 Rutgers Conference on Lie Algebras and Related Topics. Lecture Notes in Mathematics, vol. 933 pp. 130–156. Berlin-Heidelberg-New York: Springer 1982
Lepowsky, J., Milne, S.: Lie algebras and classical partition identities. Proc. Nat. Acad. Sci. U.S.A.75, 578–579 (1978)
Lepowsky, J., Milne, S.: Lie algebraic approaches to classical partition identities. Advances in Math.29, 15–59 (1978)
Lepowsky, J., Primc, M.: Standard modules for type one affine Lie algebras. Number Theory, New York, 1982. Lecture Notes in Mathematics, vol. 1052, pp. 194–251. Berlin-Heidelberg-New York: Springer 1984
Lepowsky, J., Wilson, R.L.: Construction of the affine Lie algebraA (1)1 . Comm. Math. Phys.62, 43–53 (1978)
Lepowsky, J., Wilson, R.L.: The Rogers-Ramanujan identities: Lie theoretic interpretation and proof. Proc. Nat. Acad. Sci. U.S.A.78, 699–701 (1981)
Lepowsky, J., Wilson, R.L.: A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Advances in Math.45, 21–72 (1982)
Lepowsky, J., Wilson, R.L.: A new family of algebras underlying the Rogers-Ramanujan identities and generalizations. Proc. Nat. Acad. Sci. U.S.A.78, 7254–7258 (1981)
Macdonald, I.G.: Affine root systems and Dedekind's η-function. Invent. Math.15, 91–143 (1972)
Moody, R.V.: A new class of Lie algebras. J. Algebra10, 211–230 (1968)
Moody, R.V.: Euclidean Lie algebras. Canad. J. Math.21, 1432–1454 (1969)
Segal, G.: Unitary representations of some infinite-dimensional groups. Comm. Math. Phys.80, 301–342 (1981)
Frenkel, I., Lepowsky, J., Meurman, A.: AnE 8-approach to F1. Proc. 1982 Montreal Conference on Finite Group Theory, McKay, J. (ed.). Lecture Notes in Mathematics. Berlin-Heidelberg-New York: Springer 1984 (in press)
Lepowsky, J.: Some constructions of the affine Lie algebraA (1)1 . Proc. 1982 Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, Lectures in Applied Math., vol. 21. Amer. Math. Soc. 1984
Misra, K.: Structure of certain standard modules forA (1)n and the Rogers-Ramanujan identities. J. Algebra88, 196–227 (1984)
Misra, K.: Structure of some standard modules forC (1)n . J. Algebra 90 (1984)
Lepowsky, J., Wilson, R.L.: Structure of standard modules, II: The case A (1)n , principal gradation, to appear.
Author information
Authors and Affiliations
Additional information
Both authors gratefully acknowledge the hospitality of the Institute for Advanced Study and partial support from National Science Foundation grant MCS 80-03000, the Rutgers University Faculty Academic Study Program and the Rutgers University Research Council while part of this work was carried out
Rights and permissions
About this article
Cite this article
Lepowsky, J., Wilson, R.L. The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities. Invent Math 77, 199–290 (1984). https://doi.org/10.1007/BF01388447
Issue Date:
DOI: https://doi.org/10.1007/BF01388447