Geodesic
Realization of the Universal $s\ell_q(2)$-Symmetric $R$-Operator in a Function Space for General and Exceptional Values of the Deformation Parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 2, pp. 196-223

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Based on the realization of representations of the algebra $s\ell_q(2)$ in the space of polynomials for general values of the deformation parameter $q$ and on a finite tuple of theta functions, which are a natural generalization of polynomials, we construct the eigenstates and find the related eigenvalues of the universal $R$-operator for cyclic representations corresponding to $q^N=\pm1$.
Keywords: exactly solvable models, cyclic representations, $N$th root of unity, eigenvalues.
Mots-clés : universal $R$-matrix 
@article{TMF_2003_135_2_a1,
     author = {D. R. Karakhanyan},
     title = {Realization of the {Universal} $s\ell_q(2)${-Symmetric} $R${-Operator} in a {Function} {Space} for {General} and {Exceptional} {Values} of the {Deformation} {Parameter}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {196--223},
     publisher = {mathdoc},
     volume = {135},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_2_a1/}
}
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D. R. Karakhanyan. Realization of the Universal $s\ell_q(2)$-Symmetric $R$-Operator in a Function Space for General and Exceptional Values of the Deformation Parameter. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 2, pp. 196-223. http://geodesic.mathdoc.fr/item/TMF_2003_135_2_a1/