2019
DOI: 10.1007/s00029-019-0521-8
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The circle quantum group and the infinite root stack of a curve

Abstract: In the present paper, we give a definition of the quantum group U υ (sl(S 1 )) of the circle S 1 := R/Z, and its fundamental representation. Such a definition is motivated by a realization of a quantum group U υ (sl(S 1 Q )) associated to the rational circle S 1 Q := Q/Z as a direct limit of U υ ( sl(n))'s, where the order is given by divisibility of positive integers. The quantum group U υ (sl(S 1 Q )) arises as a subalgebra of the Hall algebra of coherent sheaves on the infinite root stack X ∞ over a fixed s… Show more

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Cited by 2 publications
(2 citation statements)
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“…The infinite root stack of a log scheme was introduced in [51]: it is a limit of tame Artin stacks (Deligne-Mumford in characteristic 0) which encodes log information as stacky data. The infinite root stack captures the geometry of the underlying log scheme, and this point of view informs several recent works by the authors and their collaborators [9,46,52,50], see also [44] for recent applications to Hall algebras and quantum groups. If X is a log scheme, we denote its infinite root stack by ∞ √ X.…”
Section: Infinite Root Stacksmentioning
confidence: 63%
“…The infinite root stack of a log scheme was introduced in [51]: it is a limit of tame Artin stacks (Deligne-Mumford in characteristic 0) which encodes log information as stacky data. The infinite root stack captures the geometry of the underlying log scheme, and this point of view informs several recent works by the authors and their collaborators [9,46,52,50], see also [44] for recent applications to Hall algebras and quantum groups. If X is a log scheme, we denote its infinite root stack by ∞ √ X.…”
Section: Infinite Root Stacksmentioning
confidence: 63%
“…They carry universal roots of line bundles equipped with a section, and in [9] were used to compactify moduli of stable maps. Root stacks have since found applications in many different areas of geometry including enumerative geometry, quantum groups [26], the theory of Néron models [11], and more. From our perspective, root stacks are an essential tool to probe the geometry of log schemes.…”
Section: Introductionmentioning
confidence: 99%