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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).
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Cited in 4 Reviews
Cited 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
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\textit{V. G. Kac} et al., Adv. Math. 42, 83--112 (1981; Zbl 0476.17003)
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References:

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[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
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[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
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