Principal Hodge representations

TL;DR

This paper classifies Hodge representations of certain simple algebraic groups with specific Hodge numbers, focusing on non-type A groups and providing a detailed classification of their R-irreducible representations.

Contribution

It offers a classification of Hodge representations for non-type A absolutely simple Q-algebraic groups with Hodge numbers (1,1,...,1), filling a gap in the understanding of these structures.

Findings

Classification of R-irreducible representations for non-type A groups

Identification of limitations in classifying type A groups

Enhanced understanding of Hodge representations with specific Hodge numbers

Abstract

We study Hodge representations of absolutely simple Q-algebraic groups with Hodge numbers h = (1,1,...,1). For those groups that are not of type A, we give a classification of the R-irreducible representations; a similar classification for type A does not seem possible.