On homomorphisms into Weyl modules corresponding to partitions with two parts

Abstract

Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda ,\mu$ be partitions, where $\mu$ has two parts. We find sufficient arithmetic conditions on $p,\lambda ,\mu$ for the existence of a nonzero homomorphism $\Delta (\lambda )\to \Delta (\mu )$ of Weyl modules for the general linear group $G{L}_n(K)$. Also for each $p$ we find sufficient conditions so that the corresponding homomorphism spaces have dimension at least 2.

Typos corrected. Minor changes in Section 6 for clarity

References in corpus (2)

• On homomorphisms involving a hook Weyl module
• Relating homomorphism spaces between Specht modules of different degrees

Cited by in corpus (5)

• Presentations of Schur and Specht modules in characteristic zero
• On stability and nonvanishing of homomorphism spaces between Weyl modules
• A periodicity theorem for extensions of Weyl modules
• Relating homomorphism spaces between Specht modules of different degrees
• Total trades, intersection matrices and Specht modules