On Irreducibility of Tensor Products of Yangian Modules

Details On Irreducibility of Tensor Products of Yangian Modules On Irreducibility of Tensor Products of Yangian Modules

1997-11-30

arxiv.org/abs/q-alg/9712004v1

Internat. Math. Research Notices (1998), 125-150

Mathematics

Quantum Algebra

21 pages, AmS-TeX

Scientific paper

We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.

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