Research output: Contribution to journal › Article › peer-review

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

Research output: Contribution to journal › Article › peer-review

Huang, C, Mukhin, E, Vicedo, B & Young, C 2019, 'The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators', *Selecta Mathematica, New Series*, vol. 25, no. 4, 52. https://doi.org/10.1007/s00029-019-0498-3

Huang, C., Mukhin, E., Vicedo, B., & Young, C. (2019). The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators. *Selecta Mathematica, New Series*, *25*(4), [52]. https://doi.org/10.1007/s00029-019-0498-3

Huang C, Mukhin E, Vicedo B, Young C. The solutions of $\mathfrak{gl}_{M|N}$ Bethe ansatz equation and rational pseudodifferential operators. Selecta Mathematica, New Series. 2019 Oct 1;25(4). 52. https://doi.org/10.1007/s00029-019-0498-3

@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",

}

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 -