arXiv (Cornell University) · 2014 · 21 citations · 0 references
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Natural SciencesMathematicsPhysicsAlgebraGeometryRepresentation TheoryAbstract AlgebraGauge TheoryGroup TheoryLie AlgebrasLie GroupsQuantum Field TheoryAffine GrassmanniansAffine Lie AlgebrasGauge TransformationsKac-moody AlgebrasLie Algebra ModulesLoop AlgebrasQuantum Groups
The affine Yangian of gl_1 was recently introduced by Maulik-Okounkov. In this article, we provide a loop realization of this algebra arising naturally from the geometric actions. The similarity of the representation theories of this algebra and of the quantum toroidal algebra of gl_1 is explained by generalizing the recent result of Gautam-Toledano Laredo to this setting.