On irreducibility of tensor products of Yangian modules associated with skew Young diagrams

Details On irreducibility of tensor products of Yangian modules associated with skew Young diagrams On irreducibility of tensor products of Yangian modules associated with skew Young diagrams

2000-12-06

arxiv.org/abs/math/0012039v2

Duke Math. J. 112 (2002), 343-378

Mathematics

Quantum Algebra

29 pages, AmS-TeX, with additions to Section 4

Scientific paper

We study the tensor product $W$ of any number of "elementary" irreducible modules $V_1,...,V_k$ over the Yangian of the general linear Lie algebra. Each of these modules is determined by a skew Young diagram and a complex parameter. For any indices $i,j=1,...,k$ there is a canonical non-zero intertwining operator $A_{ij}$ between the tensor products $V_i\otimes V_j$ and $V_j\otimes V_i$. This operator is defined up to a scalar multipler. We show that the tensor product $W$ is irreducible, if and only if all operators $A_{ij}$ with $i

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