The Principal SO(1,2) Subalgebra of a Hyperbolic Kac Moody Algebra

2001/07/31 by H. Nicolai, D. I. Olive
Physics and Astronomy · #hep-th

paper · pdf

published as Lett.Math.Phys. 58 (2001) 141-152 · 13 pages, Latex. Version to be published in Letters in Mathematical Physics

arxiv created 2001/09/19 · arxiv updated 2009/11/30

Abstract

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact group SO(1,2). We exhibit the decomposition of g(A) into representations of SO(1,2); with the exception of the adjoint SO(1,2) algebra itself, all of these representations are unitary. We compute the Casimir eigenvalues; the associated ``exponents'' are complex and non-integer.

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