Vol. 292, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 293: 1
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
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