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arXiv · 2107.11842

On homomorphisms into Weyl modules corresponding to partitions with two parts

Mihalis Maliakas·Dimitra-Dionysia Stergiopoulou
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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 $GL_n(K)$. Also for each $p$ we find sufficient conditions so that the corresponding homomorphism spaces have dimension at least 2.

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Mihalis Maliakas, Dimitra-Dionysia Stergiopoulou. 2021-07-25. On homomorphisms into Weyl modules corresponding to partitions with two parts. https://doi.org/10.1017/s0017089522000246

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