Finite dimensional irreducible representations of twisted Yangians
Nov, 199759 pages
Published in:
- J.Math.Phys. 39 (1998) 5559-5600
e-Print:
- q-alg/9711022 [math.QA]
DOI:
Report number:
- CMA-047-97
View in:
Citations per year
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.References(30)
Figures(0)