KLR and Schur algebras for curves and semi-cuspidal representations

Abstract

Given a smooth curve $C$, we define and study analogues of KLR algebras and quiver Schur algebras, where quiver representations are replaced by torsion sheaves on $C$. In particular, they provide a geometric realization for certain affinized symmetric algebras. When $C={\mathbb{P}}^1$, a version of curve Schur algebra turns out to be Morita equivalent to the imaginary semi-cuspidal category of the Kronecker quiver in any characteristic. As a consequence, we argue that one should not expect to have a reasonable theory of parity sheaves for affine quivers.

51 pages

References in corpus (3)

• 2-Kac-Moody algebras
• Affine highest weight categories and affine quasihereditary algebras
• Quiver Schur algebras and cohomological Hall algebras

Cited by in corpus (1)

• Flag versions of quiver Grassmannians for Dynkin quivers have no odd cohomology