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

H. Nicolai·D. I. Olive
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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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H. Nicolai, D. I. Olive. 2001-09-19. The Principal SO(1,2) Subalgebra of a Hyperbolic Kac Moody Algebra. https://arxiv.org/abs/hep-th/0107146

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