The Principal SO ( 1 , 2 ) Subalgebra of a Hyperbolic
نویسنده
چکیده
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. July 2001 ∗Work supported in part by the European Union under Contract No. HPRN-CT-2000-0013
منابع مشابه
The Principal SO ( 1 , 2 ) Subalgebra of a Hyperbolic Kac
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 algebra 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 represe...
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