Affine tangles and irreducible exotic sheaves

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 $s{l}_{2n}$ 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.

The paper has been enhanced and replaced by arXiv:1602.00768

References in corpus (1)

• Noncommutative Counterparts of the Springer Resolution

Cited by in corpus (3)

• 2-block Springer fibers: convolution algebras and coherent sheaves
• Representations of semisimple Lie algebras in prime characteristic and noncommutative Springer resolution
• Orthogonally spherical objects and spherical fibrations