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

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 $s{l}_2$ (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].

This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/