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Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2025, Lie Theory and Its Applications in Physics, Springer Nature Singapore Pte Ltd.), p. 263-273), ISBN 978-981-97-6452-5, ISSN 2194-1009
Annotation:
In our paper (Č. Burdík, O. Navrátil. Theor. and Math. Phys. 198 (2019) 1–16) we study the highest weight representations of the RTT–algebra of the sp(4) type by the nested algebraic Bethe ansatz. For the constructions we used the RTT–algebra A~2. Now we show that our Bethe vectors of this algebra are linearly dependent and the linearly independent vectors can be constructed using Bethe vectors of the RTT–algebra of gl(2) type only. In addition, we will present relations from which similar results also follow for RTT–algebras of type sp(2n) and so(2n)
DOI:
Type:
Proceedings paper from a prestigious conference (Scopus)
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2022, Lie Theory and Its Applications in Physics, Springer Nature Singapore Pte Ltd.), p. 325-332), ISBN 978-981-19-4750-6, ISSN 2194-1009
Annotation:
This contribution continues our recent studies on the algebraic Bethe Ansatz for the RTT–algebras of sp(2n) and o(2n) types. In these studies, we faced RTT–algebras which we called An. The next step in our construction of the Bethe vectors for the RTT-algebras of type sp(2n) and o(2n) is to find the Bethe vectors for the RTT–algebras An. This paper deals with the construction of the Bethe vectors of the RTT–algebra An using the Bethe vectors of the RTT–algebra An−1.
DOI:
Type:
Proceedings paper from a prestigious conference (Scopus)
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2022, Theoretical and Mathematical Physics, 213 (1), p. 1395-1405), ISSN 0040-5779
Annotation:
We extend our recent results on the Bethe vectors for the RTT-algebra of sp(4) type. We show how the Bethe vectors can be rewritten in a different form similar to the trace formula for the Bethe vectors of the RTT-algebra of the gl(3) type.
DOI:
Type:
Article in a journal indexed in SCI Expanded
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2020, Physics of Particles and Nuclei Letters, 17 (5), p. 789-793), ISSN 1547-4771
Annotation:
We study the highest weight representations of the RTT-algebras for the R-matrix sp(q)(4) of type by the nested algebraic Bethe ansatz. It is a generalization of our study for R-matrix of sp(4).
DOI:
Type:
Article in a journal indexed in the Scopus database
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2020, Lie Theory and Its Applications in Physics, Springer Nature Singapore Pte Ltd.), p. 319-328), ISBN 978-981-15-7774-1, ISSN 2194-1009
Annotation:
We study the highest weight representations of the RTT–algebras for the R–matrix of type by the nested algebraic Bethe ansatz. It is a generalization of our study for R–matrix of and type.
DOI:
Type:
Proceedings paper from a prestigious conference (Scopus)
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.; Pošta, S.
Published:
2019, ISSN 1742-6596
Type:
Proceedings of an international conference
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2019, Theoretical and Mathematical Physics, 198 (1), p. 1-16), ISSN 0040-5779
Annotation:
We show how to formulate the algebraic nested Bethe ansatz for RTT algebras with an R-matrix of the sp(4) type. We obtain the Bethe vectors and Bethe conditions for any highest-weight representation of these RTT algebras.
DOI:
Type:
Article in a journal indexed in SCI Expanded
Authors:
doc. RNDr. Ondřej Navrátil, Ph.D.; Burdík, Č.
Published:
2018, Physics of Particles and Nuclei, 49 (5), p. 939-942), ISSN 1063-7796
Annotation:
We study the highest weight representations of the RTT-algebras for the R-matrix of sp(2n) type by the nested algebraic Bethe ansatz. For special representations these models were solved by Reshetikhin and by Martins and Ramos.
DOI:
Type:
Article in a journal indexed in SCI Expanded
Authors:
Burdík, Č.; doc. RNDr. Ondřej Navrátil, Ph.D.
Published:
2018, Physics of Atomic Nuclei, 81 (6), p. 776-780), ISSN 1063-7788
Annotation:
We study the highest weight representations of the RTT algebras for the R matrix of o(2n) type
by the nested algebraic Bethe ansatz. We show how auxiliary RTT algebra A˜ can be used to find Bethe
vectors and Bethe conditions. For special representations, in which representation of RTT algebra A˜ is
trivial, the problem was solved by Reshetikhin.
DOI:
Type:
Article in a journal indexed in SCI Expanded