Annals of K-Theory

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

Antoine Touzé

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Abstract

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.

Article information

Source
Ann. K-Theory, Volume 3, Number 2 (2018), 287-329.

Dates
Received: 9 December 2016
Revised: 4 May 2017
Accepted: 29 May 2017
First available in Project Euclid: 4 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.akt/1522807261

Digital Object Identifier
doi:10.2140/akt.2018.3.287

Mathematical Reviews number (MathSciNet)
MR3781429

Zentralblatt MATH identifier
06861675

Subjects
Primary: 20G10: Cohomology theory
Secondary: 18G15: Ext and Tor, generalizations, Künneth formula [See also 55U25]

Keywords
cup products strict polynomial functors Steinberg's tensor product theorem Schur functor

Citation

Touzé, Antoine. Connectedness of cup products for polynomial representations of $\mathrm{GL}_n$ and applications. Ann. K-Theory 3 (2018), no. 2, 287--329. doi:10.2140/akt.2018.3.287. https://projecteuclid.org/euclid.akt/1522807261


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