Skip to main content

Algebraic Structures Related to Racah Doubles

  • Conference paper
  • First Online:
Book cover Lie Theory and Its Applications in Physics (LT 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 191))

Included in the following conference series:

  • 1220 Accesses

Abstract

In Oste and Van der Jeugt, SIGMA, 12 (2016), [13], we classified all pairs of recurrence relations connecting two sets of Hahn, dual Hahn or Racah polynomials of the same type but with different parameters. We examine the algebraic relations underlying the Racah doubles and find that for a special case of Racah doubles with specific parameters this is given by the so-called Racah algebra.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. N.M. Atakishiyev, G.S. Pogosyan, L.E. Vicent, K.B. Wolf, J. Phys. A 34 (2001) 9381–9398.

    Article  MathSciNet  Google Scholar 

  2. N.M. Atakishiyev, G.S. Pogosyan, K.B. Wolf, Phys. Part. Nuclei 36 (2005) 247–265.

    Google Scholar 

  3. W.N. Bailey, Generalized hypergeometric series (Cambridge University Press, Cambridge, 1964).

    MATH  Google Scholar 

  4. T.S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications Vol. 13 (Gordon and Breach Science Publishers, New York-London-Paris, 1978).

    MATH  Google Scholar 

  5. T.S. Chihara, Boll. Un. Mat. Ital. (3) 19 (1964) 451–459.

    Google Scholar 

  6. V.X. Genest, L. Vinet, A. Zhedanov, J. Phys.: Conf. Ser. 512 (2014) 012010.

    Google Scholar 

  7. Y. Granovskii, A. Zhedanov, Zh. Eksp. Teor. Fiz 94 (1988) 49–54.

    Google Scholar 

  8. E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt, J. Phys. A 44 (2011) 265203.

    Article  Google Scholar 

  9. E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt, J. Phys. A 44 (2011) 355205.

    Article  Google Scholar 

  10. R. Koekoek, P.A. Lesky, R.F. Swarttouw, Hypergeometric orthogonal polynomials and their \(q\)-analogues (Springer-Verlag, Berlin, 2010).

    Google Scholar 

  11. F. Marcellán, J. Petronilho, Linear Algebra Appl. 220 (1997) 169–208.

    Article  Google Scholar 

  12. A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Springer-Verlag, Berlin, 1991).

    Book  MATH  Google Scholar 

  13. R. Oste, J. Van der Jeugt, SIGMA 12 (2016) 003.

    Google Scholar 

  14. S. Tsujimoto, L. Vinet, A. Zhedanov, Adv. Math. 229 4 (2012) 2123–2158.

    Article  MathSciNet  Google Scholar 

  15. A. Zhedanov, J. Approx. Theory 94 (1998) 73–106.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roy Oste .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Nature Singapore Pte Ltd.

About this paper

Cite this paper

Oste, R., Van der Jeugt, J. (2016). Algebraic Structures Related to Racah Doubles. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_43

Download citation

Publish with us

Policies and ethics