Affine tangles and irreducible exotic sheaves

2008/02/07 by Anno, Rina
#14F05 #18F99 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.0802.1070

Abstract

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories \mathcal D_2n. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of sl_2n with two equal Jordan blocks. This representation allows us to enumerate the irreducible objects in the heart of the exotic t-structure on \mathcal D_2n by crossingless matchings of 2n points on a circle. We also describe the algebra of endomorphisms of the direct sum of the irreducible objects.

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