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Pré-Publication, Document De Travail Année : 2016

LANNES' T FUNCTOR ON INJECTIVE UNSTABLE MODULES AND HARISH-CHANDRA RESTRICTION

Résumé

In the 1980's, the magic properties of the cohomology of elementary abelian groups as modules over the Steenrod algebra initiated a long lasting interaction between topology and modular representation theory in natural characteristic. The Adams-Gunawardena-Miller theorem in particular, showed that their decomposition is governed by the modular representations of the semi-groups of square matrices. Applying Lannes' T functor on the summands L P := Hom Mn(Fp) (P, H * (F p) n) defines an intriguing construction in representation theory. We show that T(L P) ∼ = L P ⊕ H * V 1 ⊗ L δ(P) , defining a functor δ from F p [M n (F p)]-projectives to F p [M n−1 (F p)]-projectives. We relate this new functor δ to classical constructions in the representation theory of the general linear groups.
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hal-01329517 , version 1 (09-06-2016)

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Vincent Franjou, Dang Ho Hai Nguyen, Lionel Schwartz. LANNES' T FUNCTOR ON INJECTIVE UNSTABLE MODULES AND HARISH-CHANDRA RESTRICTION. 2016. ⟨hal-01329517⟩
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