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

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

2008-06-11

arxiv.org/abs/0806.1976v2

SIGMA 4 (2008), 059, 11 pages

Mathematics

Representation Theory

This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrabilit

Scientific paper

10.3842/SIGMA.2008.059

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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