Skip to main content
SpringerLink
Log in

Chebyshev polynomials for a three-dimensional algebra

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

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 C3.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Dupont, Algebr. Represent. Theor., 15, 527–549 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. V. Borzov and E. V. Damaskinsky, Theor. Math. Phys., 175, 763–770 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  3. G. von Gehlen and S.-S. Roan, “The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials,” in: Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory (NATO Sci. Ser. II: Math. Phys. Chem., Vol. 35, S. Pakuliak and G. von Gehlen, eds.), Kluwer, Dordrecht (2001), pp. 155–172; arXiv:hep-th/0104144v1 (2001).

    Chapter  Google Scholar 

  4. T. H. Koornwinder, Nederl. Akad. Wetensch. Proc. Ser. A, 77, 48–66, 357–381 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  5. R. J. Beerends, Trans. Amer. Math. Soc., 328, 779–814 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  6. V. D. Lyakhovsky and Ph. V. Uvarov, J. Phys. A: Math. Theor., 46,125201(2013).

    Article  MathSciNet  ADS  Google Scholar 

  7. E. Verlinde, Nucl. Phys. B, 300, 360–376 (1988).

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  9. A. Klimyk and K. Schmüdgen, Quantum Groups and Their Representations, Springer, Berlin (1997).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. D. Lyakhovsky

Authors
  1. V. D. Lyakhovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. D. Lyakhovsky.

Additional information

This research was supported by the Russian Foundation for Basic Research (Grant No. 15-01-03148).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 1, pp. 118–126, October, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyakhovsky, V.D. Chebyshev polynomials for a three-dimensional algebra. Theor Math Phys 185, 1462–1470 (2015). https://doi.org/10.1007/s11232-015-0355-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-015-0355-2

Keywords

Search

Navigation