Symmetry Integrability and Geometry-Methods and Applications | |
Loops in SU(2), Riemann Surfaces, and Factorization, I | |
article | |
Estelle Basor1  Doug Pickrell2  | |
[1] American Institute of Mathematics;Mathematics Department, University of Arizona | |
关键词: loop group; factorization; Toeplitz operator; determinant; | |
DOI : 10.3842/SIGMA.2016.025 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
In previous work we showed that a loop $g\colon S^1 \to {\rm SU}(2)$ 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 ${\rm SU}(2)$ 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 ${\rm SL}(2,\mathbb C)$ bundle. Additionally, for such a multiloop, there is a corresponding factorization for determinants associated to the spin Toeplitz operators defined by the multiloop.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300001156ZK.pdf | 471KB | download |