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Higher representation theory

Thursday 16th April 2009 - 16:00 to 17:00
We have introduced a 2-category associated with a Kac-Moody algebra (the type A case goes back to joint work with Joe Chuang and a close version of the positive half has been introduced independently by Khovanov and Lauda). We will discuss the 2-representation theory, ie, actions of this 2-category on categories (additive, abelian, triangulated, dg...). We will present a unicity result for simple integrable 2-representations and Jordan-Holder series. We will explain the realisation of simple 2-representations as categories of sheaves on quiver varieties and deduce the description of classes of indecomposable projective modules as canonical basis elements.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons