Finite-dimensional irreducible representations of twisted Yangians

Details Finite-dimensional irreducible representations of twisted Yangians Finite-dimensional irreducible representations of twisted Yangians

1997-11-25

arxiv.org/abs/q-alg/9711022v1

J.Math.Phys. 39 (1998) 5559-5600

Physics

High Energy Physics

High Energy Physics - Theory

AMSTEX, 59 pages

Scientific paper

10.1063/1.532551

We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to the coproduct in Y(gl(N)). We give a complete description of their finite-dimensional irreducible representations. Every such representation is highest weight and we give necessary and sufficient conditions for an irreducible highest weight representation to be finite-dimensional. The result is analogous to Drinfeld's theorem for the ordinary Yangians. Its detailed proof for the A series is also reproduced. For the simplest twisted Yangians we construct an explicit realization for each finite-dimensional irreducible representation in tensor products of representations of the corresponding Lie algebras.

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