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arXiv · 2010.01419

KLR and Schur algebras for curves and semi-cuspidal representations

Ruslan Maksimau·Alexandre Minets
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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.

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BibTeXRIS

Ruslan Maksimau, Alexandre Minets. 2020-10-03. KLR and Schur algebras for curves and semi-cuspidal representations. https://doi.org/10.1093/imrn/rnac055

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