On the geometric realization of the inner product and canonical basis for quantum affine sln

McGerty, Kevin

doi:10.2140/ant.2012.6.1097

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$

Kevin McGerty

Vol. 6 (2012), No. 6, 1097–1131

DOI: 10.2140/ant.2012.6.1097

Abstract

We give a geometric interpretation of the inner product on the modified quantum group of ${\hat{s l}}_{n}$ . We also give some applications of this interpretation, including a positivity result for the inner product, and a new geometric construction of the canonical basis.

Keywords

quantum groups, canonical bases, perverse sheaves

Mathematical Subject Classification 2010

Primary: 20G42

Secondary: 20G43, 17B37

Milestones

Received: 3 October 2010

Revised: 8 May 2011

Accepted: 30 June 2011

Published: 12 August 2012

Authors

Kevin McGerty
Mathematical Institute University of Oxford 24-29 St Giles’ Oxford OX1 3LB United Kingdom

Vol. 6, No. 6, 2012