On the Gaudin and XXX models associated to Lie superalgebras
Indiana University-Purdue University Indianapolis (IUPUI) === We describe a reproduction procedure which, given a solution of the 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...
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ndltd-IUPUI-oai-scholarworks.iupui.edu-1805-234002020-07-30T05:05:54Z On the Gaudin and XXX models associated to Lie superalgebras Huang, Chenliang Mukhin, Evgeny Bleher, Pavel Roeder, Roland Tarasov, Vitaly Bethe ansatz Gaudin system supersymmetric spin chain rational differential operator difference operator Berezinian Capelli identity Duality Indiana University-Purdue University Indianapolis (IUPUI) We describe a reproduction procedure which, given a solution of the 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 gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions. We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k). The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n) and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results. We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)). To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains. 2020-07-28T16:32:53Z 2020-07-28T16:32:53Z 2020-08 Thesis http://hdl.handle.net/1805/23400 en_US CC0 1.0 Universal http://creativecommons.org/publicdomain/zero/1.0/ |
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Bethe ansatz Gaudin system supersymmetric spin chain rational differential operator difference operator Berezinian Capelli identity Duality |
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Bethe ansatz Gaudin system supersymmetric spin chain rational differential operator difference operator Berezinian Capelli identity Duality Huang, Chenliang On the Gaudin and XXX models associated to Lie superalgebras |
description |
Indiana University-Purdue University Indianapolis (IUPUI) === We describe a reproduction procedure which, given a solution of the 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 gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.
We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k).
The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n)
and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results.
We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)).
To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains. |
author2 |
Mukhin, Evgeny |
author_facet |
Mukhin, Evgeny Huang, Chenliang |
author |
Huang, Chenliang |
author_sort |
Huang, Chenliang |
title |
On the Gaudin and XXX models associated to Lie superalgebras |
title_short |
On the Gaudin and XXX models associated to Lie superalgebras |
title_full |
On the Gaudin and XXX models associated to Lie superalgebras |
title_fullStr |
On the Gaudin and XXX models associated to Lie superalgebras |
title_full_unstemmed |
On the Gaudin and XXX models associated to Lie superalgebras |
title_sort |
on the gaudin and xxx models associated to lie superalgebras |
publishDate |
2020 |
url |
http://hdl.handle.net/1805/23400 |
work_keys_str_mv |
AT huangchenliang onthegaudinandxxxmodelsassociatedtoliesuperalgebras |
_version_ |
1719333989541478400 |