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

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The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators. / Huang, Chenliang; Mukhin, Evgeny; Vicedo, Benoît; Young, Charles.

In: Selecta Mathematica, New Series, Vol. 25, No. 4, 52, 01.10.2019.

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@article{5edbd16003bc478680dcbcb726225b4f,
title = "The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators",
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. ",
keywords = "math.QA, math-ph, math.MP",
author = "Chenliang Huang and Evgeny Mukhin and Beno{\^i}t Vicedo and Charles Young",
note = "{\textcopyright} 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s00029-019-0498-3. ",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s00029-019-0498-3",
language = "English",
volume = "25",
journal = "Selecta Mathematica",
issn = "1022-1824",
publisher = "Birkhauser Verlag Basel",
number = "4",

}

RIS

TY - JOUR

T1 - The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators

AU - Huang, Chenliang

AU - Mukhin, Evgeny

AU - Vicedo, Benoît

AU - Young, Charles

N1 - © 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s00029-019-0498-3.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - math.QA

KW - math-ph

KW - math.MP

U2 - 10.1007/s00029-019-0498-3

DO - 10.1007/s00029-019-0498-3

M3 - Article

VL - 25

JO - Selecta Mathematica

JF - Selecta Mathematica

SN - 1022-1824

IS - 4

M1 - 52

ER -