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arXiv · 0806.1976

Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras

Dmitry Fuchs·Constance Wilmarth
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Abstract

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 $A_{1}^{1}$ the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154-156].

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Dmitry Fuchs, Constance Wilmarth. 2008-08-27. Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras. https://doi.org/10.3842/sigma.2008.059

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