Geometry of the analytic loop group
Quantum Algebra
2013-02-13 v2 Algebraic Geometry
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.
Cite
@article{arxiv.0812.3540,
title = {Geometry of the analytic loop group},
author = {Corrado De Concini and David Hernandez and Nicolai Reshetikhin},
journal= {arXiv preprint arXiv:0812.3540},
year = {2013}
}
Comments
30 pages. Accepted for publication in Advances in Mathematics