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Title: Quantum ordering for quantum geodesic functions of orbifold Riemann surfaces
Authors: Chekhov, Leonid
Mazzocco, Marta
Editors: Buchstaber, V.M.
Dubrovin, B.A.
Krichever, I.M.
Issue Date: 2013
Publisher: © American Mathematical Society
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.
Series/Report no.: American Mathematical Society Translations series 2;234
Abstract: 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).
Description: 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.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/17244
Publisher Link: http://www.ams.org/bookstore/trans2series
ISBN: 9781470418717
ISSN: 0065-9290
Appears in Collections:Book Chapters (Maths)

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