Finite-dimensional irreducible representations of twisted Yangians
arXiv:q-alg/9711022 · doi:10.1063/1.532551
Abstract
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.
AMSTEX, 59 pages
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