Vol. 6, No. 6, 2012

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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
Abstract

We give a geometric interpretation of the inner product on the modified quantum group of sl̂n. 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