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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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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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irk-123456789-1477222019-02-16T01:24:21Z Loops in SU(2), Riemann Surfaces, and Factorization, I Basor, E. Pickrell, D. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147722 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Basor, E. Pickrell, D. |
| spellingShingle |
Basor, E. Pickrell, D. Loops in SU(2), Riemann Surfaces, and Factorization, I Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Basor, E. Pickrell, D. |
| author_sort |
Basor, E. |
| title |
Loops in SU(2), Riemann Surfaces, and Factorization, I |
| title_short |
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_sort |
loops in su(2), riemann surfaces, and factorization, i |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147722 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT basore loopsinsu2riemannsurfacesandfactorizationi AT pickrelld loopsinsu2riemannsurfacesandfactorizationi |
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2023-05-20T17:28:08Z |
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2023-05-20T17:28:08Z |
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1796153362793627648 |