Rectangular representations and $\hat{I}»$-independence of algebraic monodromy groups

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 $\hat{I}»$-independence results on the algebraic monodromy groups of compatible systems of $\hat{I}»$-adic Galois representations of number fields.

31 pages, 8 figures, accepted by International Mathematics Research Notices