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Loops in SU(2), Riemann Surfaces, and Factorization, I
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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In previous work we showed that a loop $g\colon S^1 \to \mathrm{SU}(2)$ 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 $\mathrm{SU}(2)$ 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 $\mathrm{SL}(2,\mathbb C)$ bundle. Additionally, for such a multiloop, there is a corresponding factorization for determinants associated to the spin Toeplitz operators defined by the multiloop.
Keywords: loop group; factorization; Toeplitz operator; determinant. 
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     author = {Estelle Basor and Doug Pickrell},
     title = {Loops in {SU(2),} {Riemann} {Surfaces,} and {Factorization,~I}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a24/}
}
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Estelle Basor; Doug Pickrell. Loops in SU(2), Riemann Surfaces, and Factorization, I. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a24/

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