KLR and Schur algebras for curves and semi-cuspidal representations

Autor:	Maksimau, Ruslan, Minets, Alexandre
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory Mathematics - Algebraic Geometry
Zdroj:	Int. Math. Res. Not. 2023, No. 8, 6976-7052 (2023)
Druh dokumentu:	Working Paper
DOI:	10.1093/imrn/rnac055
Popis:	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. Comment: 51 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.01419 Zobrazit plný text záznamu View this record from Arxiv