Shifted Yangians and polynomial R-matrices

Hernandez, David; Zhang, Huafeng

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4171/PRIMS/60-1-1

Title :

Shifted Yangians and polynomial R-matrices

Author(s) :

Hernandez, David [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Zhang, Huafeng [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Publ.Res.Inst.Math.Sci.Kyoto

Pages :

Publication date :

2024

HAL domain(s) :

Physique [physics]/Physique mathématique [math-ph]

English abstract : [en]

We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. ...
Show more >We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by the representation theory of the Borel subalgebra of a quantum affine algebra and by the relevance of quantum integrable systems in this context, we prove that tensor products of prefundamental modules with irreducible modules are either cyclic or co-cyclic. This implies the existence and uniqueness of morphisms, the R-matrices, for such tensor products. We prove the R-matrices are polynomial in the spectral parameter, and we establish functional relations for the R-matrices. As applications, we prove the Jordan--Hölder property in the category O. We also obtain a proof, uniform for any finite type, that any irreducible module factorizes through a truncated shifted Yangian.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2103.10993
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Shifted Yangians and polynomial R-matrices

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