Current presentation for the super-Yangian double DY (gl(m|n)) and Bethe vectors

A. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians Y (gl(m|n) in terms of the current generators of the Yangian double DY (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 (gl(m|n)). These Bethe vectors are also shown to obey certain recursion relations which prove their equivalence. Bibliography: 30 titles.

Original languageEnglish
Pages (from-to)33-99
Number of pages67
JournalRussian Mathematical Surveys
Issue number1
Publication statusPublished - 2017


  • Bethe vector
  • Current algebra
  • Gauss decomposition
  • Monodromy matrix
  • Projection


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