dorsal/arxiv
View SchemaLanglands Reciprocity for Algebraic Surfaces
| Authors | Victor Ginzburg, Mikhail Kapranov, Eric Vasserot |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9502013 |
| URL | https://arxiv.org/abs/q-alg/9502013 |
Abstract
This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra generated by the Hecke operators turns out to be a homomorphic image of the {\it quantum toroidal algebra}. The latter is a quantization, in the spirit of Drinfeld-Jimbo, of the universal enveloping algebra of the universal central extension of a "double-loop" Lie algebra. This yields, in particular, a new geometric construction of affine quantum groups of types A, D E in terms of Hecke operators for an elliptic surface.
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"abstract": "This note is an attempt to extend \"Geometric Langlands Conjecture\" from\nalgebraic curves to algebraic surfaces. We introduce certain Hecke-type\noperators on vector bundles on an algebraic surface. The crucial observation is\nthat the algebra generated by the Hecke operators turns out to be a homomorphic\nimage of the {\\it quantum toroidal algebra}. The latter is a quantization, in\nthe spirit of Drinfeld-Jimbo, of the universal enveloping algebra of the\nuniversal central extension of a \"double-loop\" Lie algebra. This yields, in\nparticular, a new geometric construction of affine quantum groups of types A, D\nE in terms of Hecke operators for an elliptic surface.",
"arxiv_id": "q-alg/9502013",
"authors": [
"Victor Ginzburg",
"Mikhail Kapranov",
"Eric Vasserot"
],
"categories": [
"q-alg",
"alg-geom",
"math.AG",
"math.QA"
],
"title": "Langlands Reciprocity for Algebraic Surfaces",
"url": "https://arxiv.org/abs/q-alg/9502013"
},
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