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# Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces

journal contribution

posted on 2015-04-13, 12:25 authored by Leonid Chekhov, Marta MazzoccoWe determine the explicit quantum ordering for a special class of quantum geodesic functions
corresponding to geodesics joining exactly two orbifold points or holes on a non-compact Riemann
surface. We discuss some special cases in which these quantum geodesic functions form sub–
algebras of some abstract algebras defined by the reflection equation and we extend our results
to the quantisation of matrix elements of the Fuchsian group associated to the Riemann surface
in Poincar´e uniformization. In particular we explore an interesting relation between the deformed
Uq(sl2) and the Zhedanov algebra AW(3).

## History

## School

- Science

## Department

- Mathematical Sciences

## Published in

American Mathematical Society Translations series 2## Volume

234## Pages

93 - 116## Citation

CHEKHOV,L. and MAZZOCCO, M., 2013. Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces. IN: Buchstaber, V.M., Dubrovin, B.A. and Krichever, I.M. (eds). Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov's Seminar 2012-2014. American Mathematical Society, pp. 93 - 116.## Publisher

© American Mathematical Society## Version

- AM (Accepted Manuscript)

## Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/## Publication date

2013## Notes

First published in Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov's Seminar 2012-2014 in American Mathematical Society Translations series 2, volume 234 published by the American Mathematical Society.## ISBN

9781470418717## ISSN

0065-9290## Publisher version

## Book series

American Mathematical Society Translations series 2;234## Language

- en