Kac, V. G.; Kazhdan, D. A.; Lepowsky, J.; Wilson, R. L. Realization of the basic representations of the Euclidean Lie algebras. (English) Zbl 0476.17003 Adv. Math. 42, 83-112 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 67 Documents MSC: 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17B65 Infinite-dimensional Lie (super)algebras 17B35 Universal enveloping (super)algebras 17B70 Graded Lie (super)algebras 47L90 Applications of operator algebras to the sciences Keywords:Euclidean Lie algebras; highest weight representation; basic representation; principal subalgebra; infinite Heisenberg algebra PDF BibTeX XML Cite \textit{V. G. Kac} et al., Adv. Math. 42, 83--112 (1981; Zbl 0476.17003) Full Text: DOI OpenURL References: [1] Feingold, A; Lepowsky, J, The Weyl-Kac character formula and power series identities, Advances in math., 29, 271-309, (1978) · Zbl 0391.17009 [2] Garland, H, The arithmetic theory of loop algebras, J. algebra, 53, 480-551, (1978) · Zbl 0383.17012 [3] Kac, V.G, Simple irreducible graded Lie algebras of finite growth, Izv. akad. nauk SSSR ser. mat., Math. USSR-izv., 2, 1271-1311, (1968), Engl. transl. · Zbl 0222.17007 [4] Kac, V.G, Infinite-dimensional Lie algebras and Dedekind’s η-function, Funkcional. anal. i priložen., Functional anal. appl., 8, 68-70, (1974), Engl. transl. · Zbl 0299.17005 [5] 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) · Zbl 0391.17010 [6] Kac, V.G, An elucidation of “infinite-dimensional algebras… and the very strange formula”, E(1)8 and the cube root of the modular invariant j, Advances in math., 35, 264-273, (1980) · Zbl 0431.17009 [7] Kostant, B, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. math., 81, 973-1032, (1959) · Zbl 0099.25603 [8] Lepowsky, J, Macdonald-type identities, Advances in math., 27, 230-234, (1978) · Zbl 0388.17003 [9] Lepowsky, J, Generalized Verma modules, loop space cohomology and Macdonald-type identities, Ann. sci. école norm. sup., 12, 169-234, (1979) · Zbl 0414.17007 [10] Lepowsky, J, Application of the numerator formula to k-rowed plane partitions, Advances in math., 35, 179-194, (1980) · Zbl 0425.10015 [11] Lepowsky, J; Milne, S, Lie algebraic approaches to classical partition identities, Advances in math., 29, 15-59, (1978) · Zbl 0384.10008 [12] Lepowsky, J; Wilson, R.L, Construction of the affine Lie algebra A(1)1, Comm. math. phys., 62, 43-53, (1978) · Zbl 0388.17006 [13] Moody, R.V, A new class of Lie algebras, J. algebra, 10, 211-230, (1968) · Zbl 0191.03005 [14] Moody, R.V, Euclidean Lie algebras, Canad. J. math., 21, 1432-1454, (1969) · Zbl 0194.34402 [15] Frenkel, I.B; Kac, V.G, Basic representations of affine Lie algebras and dual resonance models, Invent. math., (1980) · Zbl 0493.17010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.