On the R-matrix realization of Yangians and their representations

Details On the R-matrix realization of Yangians and their representations On the R-matrix realization of Yangians and their representations

2005-11-19

arxiv.org/abs/math/0511481v1

Annales Henri Poincare, 7 (2006), 1269-1325.

Mathematics

Quantum Algebra

65 pages

Scientific paper

10.1007/s00023-006-0281-9

We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we are concerned with the algebraic structure and representations of the algebra X(a). We prove an analog of the Poincare-Birkhoff-Witt theorem for X(a) and show that the Yangian Y(a) can be realized as a subalgebra of X(a). Furthermore, we give an independent proof of the classification theorem for the finite-dimensional irreducible representations of X(a) which implies the corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit constructions for all fundamental representation of the Yangians.

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