Structure of the stringR-matrix

2008/06/18 by Алессандро Торриелли, Alessandro Torrielli
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Geometry #Law #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Representation (politics) #String (physics) #Symmetry (geometry) #Theoretical physics #Yangian #hep-th #math.QA

paper · pdf · doi:10.1088/1751-8113/42/5/055204

published as J.Phys.A42:055204,2009 · 9 pages, LaTeX; typos corrected

arxiv created 2008/06/18 · openalex publication_date 2009/01/06 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/06

Abstract

By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R -matrix, in a form that carries explicit dependence on the representation labels, the braiding factors and the spectral parameters u i . In this way, we demonstrate that there exists rewriting of its entries, such that the dependence on the spectral parameters is purely of a difference form . Namely, the latter enter only in the combination u 1 − u 2 , as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows us to spot new interesting relations among them. This permits us to package them into a practical tensorial expression, where the nondiagonal entries are taken care of by explicit combinations of symmetry algebra generators.

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