Geometry of the analytic loop group

Corrado De Concini; David Hernandez; Nicolai Reshetikhin

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arXiv · 0812.3540

Geometry of the analytic loop group

Corrado De Concini·David Hernandez·Nicolai Reshetikhin

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Abstract

We introduce and study a notion of analytic loop group with a Riemann-Hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity with non trivial central charge. We introduce a Poisson structure and study properties of its Poisson dual group. We prove that the Hopf-Poisson structure is isomorphic to the semi-classical limit of the center of the quantum affine algebra (it is a geometric realization of the center). Then the symplectic leaves, and corresponding equivalence classes of central characters, are parameterized by certain G-bundles on an elliptic curve.

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BibTeX RIS

Corrado De Concini, David Hernandez, Nicolai Reshetikhin. 2013-02-12. Geometry of the analytic loop group. https://arxiv.org/abs/0812.3540

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