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

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dc.creatorNazarov, Maxim
dc.creatorTarasov, Vitaly
dc.date2000-12-06
dc.date2000-12-07
dc.date.accessioned2026-07-07T04:39:04Z
dc.date.available2026-07-07T04:39:04Z
dc.descriptionWe 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 $i<j$ are invertible. This implies that the Yangian module $W$ is irreducible, if and only if all pairwise tensor products $V_i\otimes V_j$ with $i<j$ are irreducible. We also introduce the notion of a Durfee rank of a skew Young diagram. For an ordinary Young diagram, this is the length of its main diagonal.
dc.description29 pages, AmS-TeX, with additions to Section 4
dc.identifierhttps://arxiv.org/abs/math/0012039
dc.identifierhttp://arxiv.org/abs/math/0012039
dc.identifierDuke Math. J. 112 (2002), 343-378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60515
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleOn irreducibility of tensor products of Yangian modules associated with skew Young diagrams
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