Affine tangles and irreducible exotic sheaves

Details Affine tangles and irreducible exotic sheaves Affine tangles and irreducible exotic sheaves

2008-02-07

arxiv.org/abs/0802.1070v3

Mathematics

Algebraic Geometry

The signs in the Ext algebra have been corrected

Scientific paper

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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