Categorification of integrable representations of quantum groups

Details Categorification of integrable representations of quantum groups Categorification of integrable representations of quantum groups

2008-03-26

arxiv.org/abs/0803.3668v2

Mathematics

Representation Theory

35pages, v2: minor revisions, typo fixed

Scientific paper

We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As byproducts, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.

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