Monodromy of Galois representations and equal-rank subalgebra equivalence

2012/04/24 by Hui, Chun Yin · 3 citations
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1204.5271

Abstract

We study l-independence of monodromy groups G_l of any compatible system of l-adic representations (in the sense of Serre) of number field K assuming semisimplicity. We prove that the formal character of the derived group of the identity component of G_l is independent of l and the (complexified) Lie algebra g_l of G_l satisfies an equal-rank subalgebra equivalence for all l. This equivalence is equivalent to the l-independence of the number of A_n factors for all n belonging to 6,9,10,11,... and the parity of A₄ factors in g_l.

Cited by

• On irreducibility of certain low dimensional automorphic Galois representations
• Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
• Rectangular representations and λ-independence of algebraic monodromy groups

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