Lannes' t functor on injective unstable modules and harish-chandra restriction
Abstract
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 (P) , defining a functor from F p [M n (F p)]-projectives to F p [M n--1 (F p)]-projectives. We relate this new functor to classical constructions in the representation theory of the general linear groups.
Keywords
Cite
@article{arxiv.1606.02905,
title = {Lannes' t functor on injective unstable modules and harish-chandra restriction},
author = {Vincent Franjou and Dang Ho Hai Nguyen and Lionel Schwartz},
journal= {arXiv preprint arXiv:1606.02905},
year = {2016}
}