Geodesic
Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 227-238 
Č. Burdík; P. Ya. Grozman; D. A. Leites; A. N. Sergeev. Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 227-238. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a2/
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     title = {Realization of {Lie} algebras and superalgebras in terms of creation and annihilation operators: {I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For every finite-dimensional nilpotent complex Lie algebra or superalgebra $\mathfrak n$, we offer three algorithms for realizing it in terms of creation and annihilation operators. We use these algorithms to realize Lie algebras with a maximal subalgebra of finite codimension. For a simple finite-dimensional $\mathfrak g$ whose maximal nilpotent subalgebra is $\mathfrak n$, this gives its realization in terms of first-order differential operators on the big open cell of the flag manifold corresponding to the negative roots of $\mathfrak g$. For several examples, we executed the algorithms using the MATHEMATICA-based package SUPERLie. These realizations form a preparatory step in an explicit construction and description of an interesting new class of simple Lie (super)algebras of polynomial growth, generalizations of the Lie algebra of matrices of complex size.

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