Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications

Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications

We describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial SL(2) monodromies around singularities and trivial PSL(2) monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes–Bethe eq...

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Main Author: Dmitry Korotkin
Format: Article
Language:English
Published: Elsevier 2018-02-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321317304108
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spelling doaj-7af49355c1344684af0a4403f02a95052020-11-25T03:40:01ZengElsevierNuclear Physics B0550-32132018-02-0192729431810.1016/j.nuclphysb.2017.12.019Stieltjes–Bethe equations in higher genus and branched coverings with even ramificationsDmitry KorotkinWe describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial SL(2) monodromies around singularities and trivial PSL(2) monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes–Bethe equations. Links with branched projective structures and with Hurwitz spaces with ramifications of even order are established. We find a higher genus analog of the genus zero Yang–Yang function (the function generating accessory parameters) and describe its similarity and difference with Bergman tau-function on the Hurwitz spaces.http://www.sciencedirect.com/science/article/pii/S0550321317304108
collection DOAJ
language English
format Article
sources DOAJ
author Dmitry Korotkin
spellingShingle Dmitry Korotkin
Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
Nuclear Physics B
author_facet Dmitry Korotkin
author_sort Dmitry Korotkin
title Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
title_short Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
title_full Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
title_fullStr Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
title_full_unstemmed Stieltjes–Bethe equations in higher genus and branched coverings with even ramifications
title_sort stieltjes–bethe equations in higher genus and branched coverings with even ramifications
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
publishDate 2018-02-01
description We describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial SL(2) monodromies around singularities and trivial PSL(2) monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes–Bethe equations. Links with branched projective structures and with Hurwitz spaces with ramifications of even order are established. We find a higher genus analog of the genus zero Yang–Yang function (the function generating accessory parameters) and describe its similarity and difference with Bergman tau-function on the Hurwitz spaces.
url http://www.sciencedirect.com/science/article/pii/S0550321317304108
work_keys_str_mv AT dmitrykorotkin stieltjesbetheequationsinhighergenusandbranchedcoveringswithevenramifications
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