Connectedness of cup products for polynomial representations of $G{L}_n$ and applications

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, for example to study the cohomological behavior of the Schur functor.

3rd version. Several references added. A few typos corrected. 'Künneth condition' added in theorem 3.6, and proof rewritten hopefully in a nicer way. Section 4 reorganized - for easier reading one part of the former section is now appendix B

References in corpus (2)

• A new proof of the Mullineux conjecture
• Cohomological finite-generation for finite supergroup schemes

Cited by in corpus (2)

• On the structure of graded commutative exponential funtors
• Homological finiteness of functors on an additive category and applications