Browsing by Author "Vicedo, Benoît"

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    The solutions of glM|N Bethe ansatz equation and rational pseudodifferential operators
    (Springer, 2019) Huang, Chenliang; Mukhin, Evgeny; Vicedo, Benoît; Young, Charles; Mathematical Sciences, School of Science
    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.