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Projections of Singular Vectors of Verma Modules over Rank 2 Kac–Moody Lie Algebras
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac–Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of $sl_{2}$ (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fuchs and Malikov [Funct. Anal. Appl. 20 (1986), no. 2, 103–113]. In the simpler case of $\mathcal A_1^1$ the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154–156].
Keywords: Kac–Moody algebras; Verma modules; singular vectors. 
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     author = {Dmitry Fuchs and Constance Wilmarth},
     title = {Projections of {Singular} {Vectors} of {Verma} {Modules} over {Rank~2} {Kac{\textendash}Moody} {Lie} {Algebras}},
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Dmitry Fuchs; Constance Wilmarth. Projections of Singular Vectors of Verma Modules over Rank 2 Kac–Moody Lie Algebras. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a58/

[1] Funct. Anal. Appl., 5:1 (1971), 1–8 | DOI | MR | Zbl

[2] Feigin B. L., Fuchs D. B., “Verma modules over the Virasoro algebra”, Topology (Leningrad, 1982), Lecture Notes in Math., 1060, Springer, Berlin, 1984, 230–245 | MR

[3] Funct. Anal. Appl., 23:2 (1989), 154–156 | DOI | MR

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[6] Funct. Anal. Appl., 20:2 (1986), 103–113 | DOI | MR | Zbl