The solutions of {\mathfrak {g}}{\mathfrak {l}}_{M|N} Bethe ansatz equation and rational pseudodifferential operators

• Chenliang Huang ^[3] ; Evgeny Mukhin ^[3] ; Benoît Vicedo ^[1] ; Charles Young ^[2]
  1. [1] University of York

     University of York

     Reino Unido

     
  2. [2] University of Hertfordshire

     University of Hertfordshire

     Welwyn Hatfield, Reino Unido

     
  3. [3] IUPUI, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 4, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0498-3
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• Resumen

  • We describe a reproduction procedure which, given a solution of the glM|N Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population. To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions. We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all glM|N Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.