Loops in SU(2), Riemann Surfaces, and Factorization, I
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Loops in SU(2), Riemann Surfaces, and Factorization, I
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| Creator |
Basor, E.
Pickrell, D. |
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| 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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| Date |
2019-02-15T18:42:42Z
2019-02-15T18:42:42Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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