Vol. 292, No. 2, 2018

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Formal confluence of quantum differential operators

Bernard Le Stum and Adolfo Quirós

Vol. 292 (2018), No. 2, 427–478
Abstract

We prove that a differential operator in the usual sense is formally the limit of quantum differential operators. For this purpose, we introduce the notion of a twisted differential operator of infinite level and prove that, formally, such an object is independent of the choice of the twist. Our method provides explicit formulas.

Keywords
$q$-difference, differential operator, confluence
Mathematical Subject Classification 2010
Primary: 12H10
Milestones
Received: 7 April 2017
Accepted: 12 June 2017
Published: 17 October 2017
Authors
Bernard Le Stum
Institut de Recherche Mathématique (IRMAR)
Universite de Rennes I
Campus de Beaulieu
35042 Rennes
France
Adolfo Quirós
Departamento de Matemáticas
Universidad Autónoma de Madrid
Ciudad Universitaria de Cantoblanco
28049 Madrid
Spain