Vol. 10, No. 9, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Cluster algebras and category $\mathscr{O}$ for representations of Borel subalgebras of quantum affine algebras

David Hernandez and Bernard Leclerc

Vol. 10 (2016), No. 9, 2015–2052
DOI: 10.2140/ant.2016.10.2015
Abstract

Let O be the category of representations of the Borel subalgebra of a quantum affine algebra introduced by Jimbo and the first author. We show that the Grothendieck ring of a certain monoidal subcategory of O has the structure of a cluster algebra of infinite rank, with an initial seed consisting of prefundamental representations. In particular, the celebrated Baxter relations for the 6-vertex model get interpreted as Fomin–Zelevinsky mutation relations.

Keywords
quantum affine algebras, cluster algebras, category $\mathscr{O}$, monoidal categorification, Baxter relations\lower5pt\hbox
Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 13F60, 17B10, 82B23
Milestones
Received: 19 April 2016
Accepted: 9 August 2016
Published: 22 November 2016
Authors
David Hernandez
Institut de Mathématiques de Jussieu-Paris Rive Gauche
Université Paris-Diderot Paris 7
Bâtiment Sophie Germain, Case 7012
75205 Paris Cedex 13
France
Bernard Leclerc
Laboratoire de Mathématiques Nicolas Oresme
Université de Caen Basse-Normandie
14032 Caen
France