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Russian Mathematical Surveys, 2017, Volume 72, Issue 1, Pages 33–99
DOI: https://doi.org/10.1070/RM9754 (Mi rm9754) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors

A. A. Hutsalyuka, A. Liashykbcd, S. Z. Pakulyakaef, E. Ragoucyg, N. A. Slavnovh

a Moscow Institute of Physics and Technology
b Bogoliubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
c National Research University "Higher School of Economics"
d Skolkovo Institute of Science and Technology
e Joint Institute for Nuclear Research
f A. I. Alikhanov Institute for Theoretical and Experimental Physics
g Laboratoire d'Annecy-le-Vieux de Physique Théorique (LAPTH), Annecy-le-Vieux, France
h Steklov Mathematical Institute of Russian Academy of Sciences
English version PDF (1084 kB) Citations (24)
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DOI: https://doi.org/10.1070/RM9754
Abstract: Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians $Y(\mathfrak{gl}(m|n)$ in terms of the current generators of the Yangian double $DY(\mathfrak{gl}(m|n))$. The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the supersymmetric Bethe vectors in terms of the matrix elements of the universal monodromy matrix. Two different presentations for the Bethe vectors are obtained by using two different but isomorphic current realizations of the Yangian double $DY(\mathfrak{gl}(m|n))$. These Bethe vectors are also shown to obey certain recursion relations which prove their equivalence.
Bibliography: 30 titles.
Keywords: Bethe vector, current algebra, monodromy matrix, Gauss decomposition, projection.
Funding agency Grant number
Centre National de la Recherche Scientifique F14-2016
Ministry of Education and Science of the Russian Federation 5-100
Russian Foundation for Basic Research 14-01-00547-а
15-31-20484-мол_а_вед.
N.A.S. thanks LAPTH in Annecy-le-Vieux for their hospitality and stimulating scientific atmosphere and CNRS for partial financial support. The work of A.L. was funded by the Russian Academic Excellence Project (project 5-100) and the joint NASU-CNRS project F14-2016. The work of S.P. was supported in part by the Russian Foundation for Basic Research (grant no. 14-01-00547-a). N.A.S. was supported by the Russian Foundation for Basic Research (grant no. 15-31-20484-мол_а_вед).
Received: 29.11.2016
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 1(433), Pages 37–106
DOI: https://doi.org/10.4213/rm9754
Bibliographic databases:
Document Type: Article
UDC: 512.579
MSC: Primary 82B23; Secondary 81R50, 17B80, 17B37
Language: English
Original paper language: Russian
Citation: A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Uspekhi Mat. Nauk, 72:1(433) (2017), 37–106; Russian Math. Surveys, 72:1 (2017), 33–99
Citation in format AMSBIB
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