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Restrictions to G(đ˝p) and G(r) of rational G-modules
Published online by Cambridge University Press:Â 26 August 2011
Abstract
We fix a prime p and consider a connected reductive algebraic group G over a perfect field k which is defined over đ˝p. Let M be a finite-dimensional rational G-module M, a comodule for k[G]. We seek to somewhat unravel the relationship between the restriction of M to the finite Chevalley subgroup G(đ˝p)âG and the family of restrictions of M to Frobenius kernels G(r) âG. In particular, we confront the conundrum that if M is the Frobenius twist of a rational G-module N,M=N(1), then the restrictions of M and N to G(đ˝p) are equal whereas the restriction of M to G(1) is trivial. Our analysis enables us to compare support varieties (and the finer non-maximal support varieties) for G(đ˝p) and G(r) of a rational G-module M where the choice of r depends explicitly on M.
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- Research Article
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- Copyright Š Foundation Compositio Mathematica 2011
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