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Original language | English |
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Article number | 52 |
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Journal | Selecta Mathematica, New Series |
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Volume | 25 |
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Issue | 4 |
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Early online date | 14 Aug 2019 |
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DOIs | |
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Publication status | Published - 1 Oct 2019 |
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Abstract
We describe a reproduction procedure which, given a solution of the $\mathfrak{gl}_{M|N}$ 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 $\mathfrak{gl}_{M|N}$ Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.
Notes
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s00029-019-0498-3.
ID: 17049699