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A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. (English) Zbl 0488.17006

##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 11P81 Elementary theory of partitions 05A17 Partitions of integers (combinatorics)
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##### References:
 [1] Rota, G. -C.: Encyclopedia of mathematics and its applications. 2 (1976) [2] Block, R.; Wilson, R. L.: On filtered Lie algebras and divided power algebras. Comm. algebra 7, 571-589 (1975) · Zbl 0334.17005 [3] . Mem. amer. Math. soc. 24 (1980) [4] Feingold, A.; Lepowsky, J.: The Weyl-Kac character formula and power series identities. Adv. in math. 29, 271-309 (1978) · Zbl 0391.17009 [5] Garland, H.; Lepowsky, J.: Lie algebra homology and the macdonald-Kac formulas. Invent. math. 34, 37-76 (1976) · Zbl 0358.17015 [6] Gordon, B.: A combinatorial generalization of the Rogers-Ramanujan identities. Amer. J. Math. 83, 393-399 (1961) · Zbl 0100.27303 [7] . Adv. in math. 30, 85-136 (1978) [8] . Adv. in math. 35, 179-194 (1980) [9] Milne, S.: Lie algebraic approaches to classical partition identities. Adv. in math. 29, 15-29 (1978) · Zbl 0384.10008 [10] Lepowsky, J.; Wilson, R. L.: Construction of the affine Lie algebra $A(1)$1. Comm. math. Phys. 62, 43-53 (1978) · Zbl 0388.17006 [11] Macdonald, I. G.: Affine root systems and Dedekind’s ${\eta}$-fuction. Invent. math. 15, 91-143 (1972) · Zbl 0244.17005 [12] . Proc. amer. Math. soc. 48, 43-52 (1975) [13] Wilson, R. L.: A new family of algebras underlying the Rogers-Ramanujan identities and generalizations. Proc. nat. Acad. sci. USA 78, 7254-7258 (1981) · Zbl 0472.17005 [14] The structure of standard modules, I. Universal algebras and the Rogers-Ramanujan identities, to appear. · Zbl 0577.17009