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SIGMA, 2008, Volume 4, 059, 11 pages (Mi sigma312)  

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

Dmitry Fuchs, Constance Wilmarth

Department of Mathematics, University of California, One Shields Ave., Davis CA 95616, USA

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 $\mathcal A_1^1$ the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154–156].

Keywords: Kac–Moody algebras; Verma modules; singular vectors

DOI: https://doi.org/10.3842/SIGMA.2008.059

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Full text: http://emis.mi.ras.ru/.../059
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Bibliographic databases:

ArXiv: 0806.1976
MSC: 17B67
Received: June 29, 2008; in final form August 24, 2008; Published online August 27, 2008
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Citation: Dmitry Fuchs, Constance Wilmarth, “Projections of Singular Vectors of Verma Modules over Rank 2 Kac–Moody Lie Algebras”, SIGMA, 4 (2008), 059, 11 pp.

Citation in format AMSBIB
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\by Dmitry Fuchs, Constance Wilmarth
\paper Projections of Singular Vectors of Verma Modules over Rank~2 Kac--Moody Lie Algebras
\jour SIGMA
\yr 2008
\vol 4
\papernumber 059
\totalpages 11
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