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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147722 |
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| Cite this: | 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| _version_ | 1862559189908324352 |
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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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| first_indexed | 2025-11-25T22:46:52Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147722 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:46:52Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| 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 |
| work_keys_str_mv | AT basore loopsinsu2riemannsurfacesandfactorizationi AT pickrelld loopsinsu2riemannsurfacesandfactorizationi |