Bethe subalgebras of Uq(glˆn)Uq(gl^n) via shuffle algebras

• Boris Feigin ^[1] ; Alexander Tsymbaliu ^[2]
  1. [1] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  2. [2] Simons Center for Geometry and Physics
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 979-1011
• Idioma: inglés
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• Resumen

  • In this article, we construct certain commutative subalgebras of the big shuffle algebra of type A(1)n−1An−1(1) . This can be considered as a generalization of the similar construction for the small shuffle algebra, obtained in Feigin et al. (J Math Phys 50(9):42, 2009). We present a Bethe algebra realization of these subalgebras. The latter identifies them with the Bethe subalgebras of Uq(glˆn)Uq(gl^n) .