Loops in SU(2), Riemann Surfaces, and Factorization, I

In previous work we showed that a loop g:S¹→SU(2) has a triangular factorization if and only if the loop g has a root subgroup factorization. In this paper we present generalizations in which the unit disk and its double, the sphere, are replaced by a based compact Riemann surface with boundary, and...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2016
Автори: Basor, E., Pickrell, D.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2016
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147722
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Loops in SU(2), Riemann Surfaces, and Factorization, I / E. Basor, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Basor, E.
Pickrell, D.
author_facet Basor, E.
Pickrell, D.
citation_txt Loops in SU(2), Riemann Surfaces, and Factorization, I / E. Basor, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In previous work we showed that a loop g:S¹→SU(2) has a triangular factorization if and only if the loop g has a root subgroup factorization. In this paper we present generalizations in which the unit disk and its double, the sphere, are replaced by a based compact Riemann surface with boundary, and its double. One ingredient is the theory of generalized Fourier-Laurent expansions developed by Krichever and Novikov. We show that a SU(2) valued multiloop having an analogue of a root subgroup factorization satisfies the condition that the multiloop, viewed as a transition function, defines a semistable holomorphic SL(2,C) bundle. Additionally, for such a multiloop, there is a corresponding factorization for determinants associated to the spin Toeplitz operators defined by the multiloop.
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language English
last_indexed 2025-11-25T22:46:52Z
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record_format dspace
spelling Basor, E.
Pickrell, D.
2019-02-15T18:42:42Z
2019-02-15T18:42:42Z
2016
Loops in SU(2), Riemann Surfaces, and Factorization, I / E. Basor, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 21 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 22E67; 47A68; 47B35
DOI:10.3842/SIGMA.2016.025
https://nasplib.isofts.kiev.ua/handle/123456789/147722
In previous work we showed that a loop g:S¹→SU(2) has a triangular factorization if and only if the loop g has a root subgroup factorization. In this paper we present generalizations in which the unit disk and its double, the sphere, are replaced by a based compact Riemann surface with boundary, and its double. One ingredient is the theory of generalized Fourier-Laurent expansions developed by Krichever and Novikov. We show that a SU(2) valued multiloop having an analogue of a root subgroup factorization satisfies the condition that the multiloop, viewed as a transition function, defines a semistable holomorphic SL(2,C) bundle. Additionally, for such a multiloop, there is a corresponding factorization for determinants associated to the spin Toeplitz operators defined by the multiloop.
This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices,
 Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy.
 The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Loops in SU(2), Riemann Surfaces, and Factorization, I
Article
published earlier
spellingShingle Loops in SU(2), Riemann Surfaces, and Factorization, I
Basor, E.
Pickrell, D.
title Loops in SU(2), Riemann Surfaces, and Factorization, I
title_full Loops in SU(2), Riemann Surfaces, and Factorization, I
title_fullStr Loops in SU(2), Riemann Surfaces, and Factorization, I
title_full_unstemmed Loops in SU(2), Riemann Surfaces, and Factorization, I
title_short Loops in SU(2), Riemann Surfaces, and Factorization, I
title_sort loops in su(2), riemann surfaces, and factorization, i
url https://nasplib.isofts.kiev.ua/handle/123456789/147722
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