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- W3098189819 abstract "We define weak 2-categories of finite dimensional algebras with bimodules, along with collections of operators $mathbb{O}_{(c,x)}$ on these 2-categories. We prove that special examples $mathbb{O}_p$ of these operators control all homological aspects of the rational representation theory of the algebraic group $GL_2$, over a field of positive characteristic. We prove that when $x$ is a Rickard tilting complex, the operators $mathbb{O}_{(c,x)}$ honour derived equivalences, in a differential graded setting. We give a number of representation theoretic corollaries, such as the existence of tight $mathbb{Z}_+$-gradings on Schur algebras $S(2,r)$, and the existence of braid group actions on the derived categories of blocks of these Schur algebras." @default.
- W3098189819 created "2020-11-23" @default.
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- W3098189819 date "2009-10-27" @default.
- W3098189819 modified "2023-10-15" @default.
- W3098189819 title "Homotopy, homology, and GL<sub>2</sub>" @default.
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- W3098189819 doi "https://doi.org/10.1112/plms/pdp040" @default.
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