The solutions of \mathfrakgl_M|N Bethe ansatz equation and rational pseudodifferential operators

2018/09/05 by Chenliang Huang, E. Mukhin, Huang, Chenliang +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1809.01279

openalex publication_date 2018/09/05 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

We describe a reproduction procedure which, given a solution of the \mathfrakgl_M|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 \mathfrakgl_M|N Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.

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