Chebyshev polynomials for a three-dimensional algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 118-126 Cet article a éte moissonné depuis la source Math-Net.Ru

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We use the direct correspondence between anti-invariant Weyl functions and multivariate Chebyshev polynomials, which allows obtaining the Chebyshev polynomials themselves. We illustrate the obtained results with polynomials for the algebra $C_3$.
Keywords: irreducible representation of an algebra, Chebyshev polynomial.
Mots-clés : singular element
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V. D. Lyakhovsky. Chebyshev polynomials for a three-dimensional algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 118-126. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a10/

[1] G. Dupont, Algebr. Represent. Theor., 15:3, 527–549 | DOI | MR | Zbl

[2] V. V. Borzov, E. V. Damaskinskii, TMF, 175:3 (2013), 379–387 | DOI | DOI | MR | Zbl

[3] G. von Gehlen, S.-S. Roan, “The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials”, Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory (Kiev, 2000), NATO Science Series II: Mathematics, Physics and Chemistry, 35, eds. S. Pakuliak, G. von Gehlen, Kluwer, Dordrecht, 2001, 155–172, arXiv: hep-th/0104144 | DOI | MR | Zbl

[4] T. H. Koornwinder, Nederl. Akad. Wetensch. Proc. Ser. A, 77 (1974), 48–66 ; 357–381 | DOI | Zbl | MR | Zbl

[5] R. J. Beerends, “Chebyshev polynomials in several variables and the radial part Laplace–Beltrami operator”, Trans. Amer. Math. Soc., 328:2 (1991), 779–814 | DOI | MR | Zbl

[6] V. D. Lyakhovsky, Ph. V. Uvarov, J. Phys. A: Math. Theor., 46:12 (2013), 125201, 22 pp. | DOI | MR | Zbl

[7] E. Verlinde, Nucl. Phys. B, 300:3 (1988), 360–376 | DOI | MR | Zbl

[8] B. Ryland, “Multivariate Chebyshev approximation”, Manifolds and Geometric Integration Colloquia MaGIC-2008 (Renon, Bolzano, Italy, February 18–21, 2008) www.math.ntnu.no/num/magic/2008

[9] A. Klimyk, K. Schmüdgen, Quantum Groups and Their Representations, Springer, Berlin, 1997 | DOI | MR | Zbl