Geodesic
Scalar products in models with a~$GL(3)$ trigonometric $R$-matrix: Highest coefficient
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 363-389

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We study quantum integrable models with a $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of bilinear combinations of the highest coefficients. We show that there exist two different highest coefficients in the models with a $GL(3)$ trigonometric $R$-matrix. We obtain various representations for the highest coefficients in terms of sums over partitions. We also prove several important properties of the highest coefficients, which are necessary for evaluating the scalar products.
Keywords: nested Bethe ansatz, highest coefficient.
Mots-clés : scalar product 
@article{TMF_2014_178_3_a3,
     author = {S. Z. Pakulyak and E. Ragoucy and N. A. Slavnov},
     title = {Scalar products in models with a~$GL(3)$ trigonometric $R$-matrix: {Highest} coefficient},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {363--389},
     publisher = {mathdoc},
     volume = {178},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_3_a3/}
}
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S. Z. Pakulyak; E. Ragoucy; N. A. Slavnov. Scalar products in models with a~$GL(3)$ trigonometric $R$-matrix: Highest coefficient. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 363-389. http://geodesic.mathdoc.fr/item/TMF_2014_178_3_a3/