Schur asymptotics of Veronese syzygies

Abstract

We study the asymptotic behavior of Veronese syzygies as representations of the general linear group. For a fixed homological degree p of the syzygies, we describe the exact asymptotic growth for the number of distinct irreducible representations and for the number of irreducible representations also counting multiplicities. This shows that asymptotically Veronese syzygies have a very rich algebraic and representation-theoretic structure as the degree of the embedding grows.