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Canonical bases and higher representation theory

Published online by Cambridge University Press:  07 October 2014

Ben Webster*
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22908, USA email bwebster@virginia.edu
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Abstract

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This paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the whole quantized universal enveloping algebra is given by the classes of the indecomposable 1-morphisms in a categorification when the associated Lie algebra is of finite type and simply laced. We also introduce natural categories whose Grothendieck groups correspond to the tensor products of lowest- and highest-weight integrable representations. This generalizes past work of the author’s in the highest-weight case.

Type
Research Article
Copyright
© The Author 2014 

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