Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 059, 11 pages      arXiv:0806.1976      http://dx.doi.org/10.3842/SIGMA.2008.059
Contribution to the Special Issue on Kac-Moody Algebras and Applications

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

Dmitry Fuchs and Constance Wilmarth
Department of Mathematics, University of California, One Shields Ave., Davis CA 95616, USA

Received June 29, 2008, in final form August 24, 2008; Published online August 27, 2008

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 sl2 (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 A11 the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154–156].

Key words: Kac-Moody algebras; Verma modules; singular vectors.

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References

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  2. Feigin B.L., Fuchs D.B., Verma modules over the Virasoro algebra, in Topology (Leningrad, 1982), Lecture Notes in Math., Vol. 1060, Springer, Berlin, 1984, 230-245.
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