Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces
journal contributionposted on 2015-04-13, 12:25 authored by Leonid Chekhov, Marta Mazzocco
We 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).
- Mathematical Sciences
Published inAmerican Mathematical Society Translations series 2
Pages93 - 116
CitationCHEKHOV,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
- AM (Accepted Manuscript)
Publisher statementThis 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/
NotesFirst 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.
Book seriesAmerican Mathematical Society Translations series 2;234