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On Irreducibility of Tensor Products of Yangian Modules

Maxim Nazarov·Vitaly Tarasov
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Abstract

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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BibTeXRIS

Maxim Nazarov, Vitaly Tarasov. 1997-11-30. On Irreducibility of Tensor Products of Yangian Modules. https://arxiv.org/abs/q-alg/9712004

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