Representations of simple Lie algebras with vectors having a zero stationary subalgebra

Abstract

The paper solves the problem of describing the representations V of compact Lie groups G and vectors v ∈ V with single stationary subgroups. It builds the classification of the representation of simple Lie algebras with vectors having a zero stationary subalgebra. If the codimension of the submanifold M 0 of dimension m in an N-dimensional Euclidean space RN is less than the dimension and the group G is simple, then all these cases are described in the corresponding tables in sections 3 and 4.