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644,709
LOOP GROUPS AND SURFACES WITH SYMMETRIES
"... For more than ten years now the loop group method has been employed sucessfully in the construction of ”integrable surfaces ” in R3, S3 and H3 (see e.g. [3] and references there). Much of the effort went into finding the right setup and in proving basic theorems, in particular with regard to how to ..."
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For more than ten years now the loop group method has been employed sucessfully in the construction of ”integrable surfaces ” in R3, S3 and H3 (see e.g. [3] and references there). Much of the effort went into finding the right setup and in proving basic theorems, in particular with regard to how
WILLMORE IMMERSIONS and Loop Groups
, 1998
"... We propose a characterisation of Willmore immersions inspired from the works of R. Bryant on Willmore surfaces and J. Dorfmeister, F. Pedit, H.Y. Wu on harmonic maps between a surface and a compact homogeneous manifold using moving frames and loop groups. We use that formulation in order to constru ..."
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Cited by 14 (1 self)
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We propose a characterisation of Willmore immersions inspired from the works of R. Bryant on Willmore surfaces and J. Dorfmeister, F. Pedit, H.Y. Wu on harmonic maps between a surface and a compact homogeneous manifold using moving frames and loop groups. We use that formulation in order
LOOP GROUPS AND HOLOMORPHIC BUNDLES
, 812
"... Abstract. This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of Gbundles with additional flag structure along a line is proven ..."
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Abstract. This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of Gbundles with additional flag structure along a line
THE LOOP GROUP AND THE COBAR CONSTRUCTION
, 903
"... Abstract. We prove that for any 1reduced simplicial set X, Adams ’ cobar construction ΩCX on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX. In order to prove this result, we extend the definition of the cobar constr ..."
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Cited by 5 (3 self)
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Abstract. We prove that for any 1reduced simplicial set X, Adams ’ cobar construction ΩCX on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX. In order to prove this result, we extend the definition of the cobar
GEOMETRY OF THE ANALYTIC LOOP GROUP
, 812
"... Abstract. We introduce and study a notion of analytic loop group with a RiemannHilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity Uǫ(ˆg) with non trivial central charge. We introduce a Poisson structure and study properties of its Poisson dual ..."
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Abstract. We introduce and study a notion of analytic loop group with a RiemannHilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity Uǫ(ˆg) with non trivial central charge. We introduce a Poisson structure and study properties of its Poisson dual
From loop groups to 2groups
 HHA
"... We describe an interesting relation between Lie 2algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the ‘Jacobiator’. Similarly, a Lie 2gr ..."
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Cited by 49 (16 self)
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We describe an interesting relation between Lie 2algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the ‘Jacobiator’. Similarly, a Lie 2
Periodic Instantons and the Loop Group
"... We construct a large class of periodic instantons. Conjecturally we produce all periodic instantons. This confirms a conjecture of Garland and Murray that relates periodic instantons to orbits of the loop group acting on an extension of its Lie algebra. AMS classification: 81T13, 53C07, 55P10 1 Int ..."
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Cited by 4 (1 self)
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We construct a large class of periodic instantons. Conjecturally we produce all periodic instantons. This confirms a conjecture of Garland and Murray that relates periodic instantons to orbits of the loop group acting on an extension of its Lie algebra. AMS classification: 81T13, 53C07, 55P10 1
FUSION RINGS OF LOOP GROUP REPRESENTATIONS
, 901
"... Abstract. We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups. ..."
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Cited by 3 (0 self)
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Abstract. We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.
Twisted Ktheory and Loop groups
 Proceedings of the International Congress of Mathematicians, Vol. III (Beijing
"... Abstract. Twisted Ktheory has received much attention recently in both mathematics and physics. We describe some models of twisted Ktheory, both topological and geometric. Then we state a theorem which relates representations of loop groups to twisted equivariant Ktheory. This is joint work with ..."
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Cited by 23 (2 self)
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Abstract. Twisted Ktheory has received much attention recently in both mathematics and physics. We describe some models of twisted Ktheory, both topological and geometric. Then we state a theorem which relates representations of loop groups to twisted equivariant Ktheory. This is joint work
THE ORDER OF CURVATURE OPERATORS ON LOOP GROUPS
, 909
"... Abstract. For loop groups (free and based), we compute the exact order of the curvature operator of the LeviCivita connection depending on a Sobolev space parameter. This extends results of Freed [1] and MaedaRosenbergTorres [4]. 1. ..."
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Abstract. For loop groups (free and based), we compute the exact order of the curvature operator of the LeviCivita connection depending on a Sobolev space parameter. This extends results of Freed [1] and MaedaRosenbergTorres [4]. 1.
Results 1  10
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644,709