Tilting modules and highest weight theory for reduced enveloping algebras

2023/08/24 by Westaway, Matthew
#17B45 #17B50 #FOS: Mathematics #Primary: 17B10 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary: 17B35

paper · doi:10.48550/arxiv.2308.12768

Abstract

Let G be a reductive algebraic group over an algebraically closed field of characteristic p>0, and let \mathfrak g be its Lie algebra. Given χ∈\mathfrak g^* in standard Levi form, we study a category \mathscr C_χ of graded representations of the reduced enveloping algebra U_χ(\mathfrak g). Specifically, we study the effect of translation functors and wall-crossing functors on various highest-weight-theoretic objects in \mathscr C_χ, including tilting modules. We also develop the theory of canonical Δ-flags and ∇-sections of Δ-flags, in analogy with similar concepts for algebraic groups studied by Riche and Williamson.

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