Rectangular representations and $\lambda$-independence of algebraic monodromy groups

Chun-Yin Hui; Wonwoong Lee

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arXiv · 2506.21941

Rectangular representations and $\lambda$-independence of algebraic monodromy groups

Chun-Yin Hui·Wonwoong Lee

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Abstract

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we obtain new $\lambda$-independence results on the algebraic monodromy groups of compatible systems of $\lambda$-adic Galois representations of number fields.

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Chun-Yin Hui, Wonwoong Lee. 2025-06-27. Rectangular representations and $\lambda$-independence of algebraic monodromy groups. https://arxiv.org/abs/2506.21941

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