Subgroups Of Simple Algebraic Groups Containing Regular Tori, And Irreducible Representations With Multiplicity 1 Non-Zero Weights

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear 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.