Rectangular representations and λ-independence of algebraic monodromy groups

2025/06/27 by Hui, Chun-Yin, Lee, Wonwoong
#11F22 #11F70 #11F80 #17B10 #20G05 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.21941

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 λ-independence results on the algebraic monodromy groups of compatible systems of λ-adic Galois representations of number fields.

Citations

• Monodromy and irreducibility of type A₁ automorphic Galois representations
• Monodromy of four dimensional irreducible compatible systems of Q
• Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
• On the rationality of algebraic monodromy groups of compatible systems
• On the rationality of certain type A Galois representations
• Variations on a theorem of Tate
• Monodromy of Galois representations and equal-rank subalgebra equivalence
• Potential automorphy and change of weight

Related

• Monodromy of Galois representations and equal-rank subalgebra equivalence
• Independence of Algebraic Monodromy Groups in Compatible Systems
• Comparison of component groups of ℓ-adic and mod ℓ monodromy groups
• Monodromy and irreducibility of type A₁ automorphic Galois representations
• Specialization of monodromy group and l-independence