Classifying representations of finite classical groups of Lie type of dimension up to ℓ⁴

2024/01/21 by Luis Gutiérrez Frez, Frez, Luis Gutiérrez, Adrián Zenteno +1
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2401.11367

Abstract

Let G be a finite classical group of Lie type of rank ℓ, defined over a field of characteristic p>2. In this work, we classify the irreducible representations of G whose dimensions are bounded by a constant proportional to ℓ, and splits into two cases according to G is of type A_ℓ or not. Furthermore, we discuss explicit formulas for computing the dimensions of such representations. The motivation for this work arises, in part, from a desire to obtain new results on two classical problems concerning Galois representations: the large image conjecture for automorphic Galois representations and the inverse Galois problem. We conclude the paper by giving some remarks on potential implications in these addresses.

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