Geodesic
Constructing Representations of the Nonstandardly Deformed Algebra $s\ell_\xi(2)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 2, pp. 209-224

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The generators of the algebra $s\ell_\xi(2)$, which result from the nonstandard (Jordanian) deformation of the algebra $s\ell(2)$, are realized in the form of finite-difference operators acting in a function space. This allows realizing arbitrary-dimensional representations of $s\ell_\xi(2)$ in the polynomial space that are in one-to-one correspondence with usual matrices of an appropriate dimension. We discuss using the suggested realization to construct and investigate the universal $R$-matrix invariant with respect to the action of the algebra $s\ell_\xi(2)$. 
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     author = {D. R. Karakhanyan},
     title = {Constructing {Representations} of the {Nonstandardly} {Deformed} {Algebra} $s\ell_\xi(2)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {209--224},
     publisher = {mathdoc},
     volume = {138},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_2_a2/}
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D. R. Karakhanyan. Constructing Representations of the Nonstandardly Deformed Algebra $s\ell_\xi(2)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 2, pp. 209-224. http://geodesic.mathdoc.fr/item/TMF_2004_138_2_a2/