Special Seminar

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories $D_n$. 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 $D_n$ by crossingless matchings of $2n$ points on a circle. We also describe the algebra of endomorphisms of the direct sum of the irreducible objects. This algebra, as conjectured in 2006 by Paul Seidel, can be described as a variant of Khovanov's arc algebra.