#### 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 ${\stackrel{̂}{\mathfrak{s}\mathfrak{l}}}_{n}$. 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