Skip to main content
Log in

Noncommutative Hypergeometry

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barnes, E.W.: The genesis of the double gamma function. Proc. London Math. Soc. 31, 358–381 (1899)

    Google Scholar 

  2. Bytsko, A.G., Teschner, J.: R-operator, co-product and Haar-measure for the modular double of . Commun. Math. Phys. 240 , 171–196 (2003)

    Google Scholar 

  3. Faddeev, L.: Discrete Heisenberg-Weyl group and modular group. Lett. Math. Phys. 34, 249–254 (1995)

    Google Scholar 

  4. Faddeev, L.: Modular double of a quantum group. Math. Phys. Stud. 21, 149–156 (2000)

    Google Scholar 

  5. Faddeev, L., Kashaev, R., Volkov, A.Yu.: Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality. Commun. Math. Phys. 219, 199–219 (2001)

    Google Scholar 

  6. Fateev, V., Zamolodchikov, A.: Selfdual solutions of the star triangle relations in Z(N) models. Phys. Lett. A92, 37–39 (1982)

    Google Scholar 

  7. Kashaev, R.: On the spectrum of Dehn twists in quantum Teichmuller theory. http://arxiv. org/list/math.QA/0008148, 2000

  8. Kharchev, S., Lebedev, D., Semenov-Tian-Shansky, M.: Unitary representations of , the modular double, and the multiparticle q-deformed Toda chains. Commun. Math. Phys. 225, 573–609 (2003)

    Google Scholar 

  9. Koornwinder, T.: Special functions and q-commuting variables. In: Special Functions, q-Series and Related Topics, Fields Institute Communicates 14, Providence, RI: Amer. Math. Soc., 1997, pp. 131–166

  10. Ponsot, B., Teschner, J.: Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of . Commun. Math. Phys. 224, 613–655 (2001)

    Google Scholar 

  11. Ruijsenaars, S. N. M.: On Barnes’ multiple zeta and gamma functions. Adv. in Math. 156, 107–132 (2000)

    Google Scholar 

  12. Schützenberger, M.-P.: Une interprètation de certaines solutions de l’èquation fonctionelle: F(x+y)=F(x)F(y). C. R. Acad. Sci. Paris 236, 352–353 (1953)

    Google Scholar 

  13. Shintani, T.: On a Kronecker limit formula for real quadratic fields. J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 24, 167–199 (1977)

    Google Scholar 

  14. Volkov, A. Yu.: Beyond the ‘Pentagon identity’. Lett. Math. Phys. 39, 393–397 (1997)

    Google Scholar 

  15. Woronowicz, S.L.: Quantum exponential function. Rev. Math. Phys. 136, 873–920 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by L. Takhtajan

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volkov, A. Noncommutative Hypergeometry. Commun. Math. Phys. 258, 257–273 (2005). https://doi.org/10.1007/s00220-005-1342-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-005-1342-5

Keywords

Navigation