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 U∈(ĝ) 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 U∈(ĝ) (it is a geometric realization of the center). Then the symplectic leaves, and corresponding equivalence classes of central characters of U∈(ĝ), are parameterized by certain G-bundles on an elliptic curve. © 2013 Elsevier Ltd.

Geometry of the analytic loop group / DE CONCINI, Corrado; David, Hernandez; Reshetikhin, Nicolai. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 238:(2013), pp. 290-321. [10.1016/j.aim.2013.02.007]

Geometry of the analytic loop group

DE CONCINI, Corrado;
2013

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 U∈(ĝ) 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 U∈(ĝ) (it is a geometric realization of the center). Then the symplectic leaves, and corresponding equivalence classes of central characters of U∈(ĝ), are parameterized by certain G-bundles on an elliptic curve. © 2013 Elsevier Ltd.
2013
quantum groups at roots of 1; riemann-hilbert factorization; representations of quantum affine algebras; g-bundles on an elliptic curve; loop groups; poisson-lie groups
01 Pubblicazione su rivista::01a Articolo in rivista
Geometry of the analytic loop group / DE CONCINI, Corrado; David, Hernandez; Reshetikhin, Nicolai. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 238:(2013), pp. 290-321. [10.1016/j.aim.2013.02.007]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/515799
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