Homotopy, homology and GL2

Vanessa Miemietz, Will Turner

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We define weak 2-categories of finite-dimensional algebras with bimodules, along with collections of operators ¿(c, x) on these 2-categories. We prove that special examples ¿p of these operators control all homological aspects of the rational representation theory of the algebraic group GL2, over a field of positive characteristic. We prove that when x is a Rickard tilting complex, the operators ¿(c, x) honour derived equivalences in a differential graded setting. We give a number of representation theoretic corollaries, such as the existence of tight 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.
Original languageEnglish
Pages (from-to)585-606
Number of pages22
JournalProceedings of the London Mathematical Society
Volume100
Issue number2
Early online date27 Oct 2009
DOIs
Publication statusPublished - Mar 2010

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