Vol. 3, No. 2, 2018

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Connectedness of cup products for polynomial representations of $\mathrm{GL}_n$ and applications

Antoine Touzé

Vol. 3 (2018), No. 2, 287–329

We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg tensor product theorem. Our connectedness bounds for cup product maps depend on numerical invariants which seem also relevant to other problems, such as the cohomological behavior of the Schur functor.

cup products, strict polynomial functors, Steinberg's tensor product theorem, Schur functor
Mathematical Subject Classification 2010
Primary: 20G10
Secondary: 18G15
Received: 9 December 2016
Revised: 4 May 2017
Accepted: 29 May 2017
Published: 24 March 2018
Antoine Touzé
Laboratoire Painlevé
Université de Lille 1 – Sciences et Technologies
Cité Scientifique
Villeneuve d’Ascq