Subgroups of simple algebraic groups containing regular tori, and irreducible representations with multiplicity 1 non-zero weights

TL;DR

This paper classifies maximal subgroups of simple algebraic groups containing regular tori and characterizes irreducible representations with all non-zero weights of multiplicity one, advancing understanding of algebraic group structure.

Contribution

It provides new classifications of subgroups with regular tori and identifies irreducible representations with simple weight multiplicity patterns.

Findings

Maximal subgroups containing regular tori are classified.

Irreducible representations with non-zero weights of multiplicity one are characterized.

Results offer insights into the structure of simple algebraic groups.

Abstract

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independent interest. In particular, we determine the irreducible representations of simple algebraic groups whose non-zero weights occur with multiplicity 1.