Contraction par Frobenius et modules de Steinberg

2017/07/04 by Gros, Michel, Kaneda, Masaharu
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1707.00960

Abstract

For a reductive group G defined over an algebraically closed field of positive characteristic, we show that the Frobenius contraction functor of G-modules is right adjoint to the Frobenius twist of the modules tensored with the Steinberg module twice. It follows that the Frobenius contraction functor preserves injectivity, good filtrations, but not semisiplicity.

Related

• Contraction par Frobenius de G-modules
• The Steinberg linkage class for a reductive algebraic group
• Reductive groups and Steinberg maps
• Irreducibility of Infinite Dimensional Steinberg Modules of Reductive Groups with Frobenius Maps
• Complete reducibility and Steinberg endomorphisms