Geometry of the analytic loop group

DOI10.1016/j.aim.2013.02.007zbMath1343.17009arXiv0812.3540OpenAlexW2148589441WikidataQ101247449 ScholiaQ101247449MaRDI QIDQ387890

Corrado De Concini, Nicolai Reshetikhin, David Hernandez

Publication date: 17 December 2013

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.3540

zbMATH Keywords

Poisson-Lie groupsloop groups\(G\)-bundles on an elliptic curvequantum groups at roots of 1representations of quantum affine algebrasRiemann-Hilbert factorization

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Loop groups and related constructions, group-theoretic treatment (22E67) Elliptic curves (14H52) Poisson algebras (17B63)

Cites Work

• Local analytic classification of \(q\)-difference equations with \(|q| = 1\)
• Moduli spaces of curves and representation theory
• Principal \(G\)-bundles over elliptic curves
• About \(G\)-bundles over elliptic curves
• A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
• Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles
• Representations of quantum groups at even roots of unity
• Central extensions of current groups in two dimensions
• Convex bases of PBW type for quantum affine algebras
• The highest coefficient of \(\text{det}H_ \eta\) and the center of the specialization at odd roots of unity for untwisted affine quantum algebras
• Stable principal bundles on a compact Riemann surface
• The \(q\)-characters at roots of unity
• The \(t\)-analogs of \(q\)-characters at roots of unity for quantum affine algebras and beyond
• Quasitriangularity of quantum groups at roots of 1
• Spherical functions on affine Lie groups
• Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras
• Localization of modules for a semisimple Lie algebra in prime characteristic (with an appendix by R. Bezrukavnikov and S. Riche, Computation for \(\text{sl}(3))\)
• Hopf algebras with trace and representations
• Stable and unitary vector bundles on a compact Riemann surface
• Quiver varieties and \(t\)-analogs of \(q\)-characters of quantum affine algebras
• Localization for quantum groups at a root of unity
• Vector Bundles Over an Elliptic Curve
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
• Equations aux q-differences et fibres vectoriels holomorphes sur la courbe elliptique C^*/q^Z
• Le centre des algèbres de coordonnées des groupes quantiques aux racines $p\sp \alpha$-ièmes de l'unité
• Conjugacy classes in loop groups and G-bundles on elliptic curves
• Finite-dimensional representations of quantum affine algebras at roots of unity
• Introduction to quantum groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item