Geodesic
Bethe vectors for orthogonal integrable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 153-174

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider quantum integrable models associated with the $\mathfrak{so}_3$ algebra and describe Bethe vectors of these models in terms of the current generators of the $\mathcal{D}Y(\mathfrak{so}_3)$ algebra. To implement this program, we use an isomorphism between the $R$-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type $B$-, $C$-, and $D$-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the $\mathfrak{so}_3$ algebra.
Keywords: Yangian of a simple Lie algebra, Yangian double, algebraic Bethe ansatz. 
@article{TMF_2019_201_2_a1,
     author = {A. N. Liashyk and S. Z. Pakuliak and E. Ragoucy and N. A. Slavnov},
     title = {Bethe vectors for orthogonal integrable models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {153--174},
     publisher = {mathdoc},
     volume = {201},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a1/}
}
TY  - JOUR
AU  - A. N. Liashyk
AU  - S. Z. Pakuliak
AU  - E. Ragoucy
AU  - N. A. Slavnov
TI  - Bethe vectors for orthogonal integrable models
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 153
EP  - 174
VL  - 201
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a1/
LA  - ru
ID  - TMF_2019_201_2_a1
ER  - 
%0 Journal Article
%A A. N. Liashyk
%A S. Z. Pakuliak
%A E. Ragoucy
%A N. A. Slavnov
%T Bethe vectors for orthogonal integrable models
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 153-174
%V 201
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a1/
%G ru
%F TMF_2019_201_2_a1
A. N. Liashyk; S. Z. Pakuliak; E. Ragoucy; N. A. Slavnov. Bethe vectors for orthogonal integrable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 153-174. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a1/