A Classification of the Principal Nilpotent Pairs in Simple Lie Algebras and Related Problems (original) (raw)

The paper presents a comprehensive classification of principal nilpotent pairs in classical simple Lie algebras, extending the work of V. Ginzburg. These pairs, characterized by their minimal simultaneous centralizer dimension, play a key role in the representation theory of these algebras. The classification hinges on combinatorial structures known as skew-graphs, mapping G-orbits of distinguished pairs to these graphs. The authors also address the finiteness problem for such pairs and provide insights into related distinctions among various simple Lie algebras.