Huang, ChenliangMukhin, EvgenyVicedo, BenoîtYoung, Charles2020-02-202020-02-202019Huang, C., Mukhin, E., Vicedo, B. et al. The solutions of glM|N Bethe ansatz equation and rational pseudodifferential operators. Sel. Math. New Ser. 25, 52 (2019). https://doi.org/10.1007/s00029-019-0498-3https://hdl.handle.net/1805/22101We 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.enPublisher Policyreproduction procedureBethe ansatz equationrational pseudodifferential operatorsArticle