Mathematical researches of D. P. Zhelobenko

TL;DR

This paper reviews the significant mathematical contributions of Dmitry Petrovich Zhelobenko, focusing on his work in Lie groups, their representations, and spectral analysis, highlighting his influence in the field.

Contribution

It provides a comprehensive overview of Zhelobenko's research, emphasizing his classification of irreducible representations and spectral analysis of representations.

Findings

Classified all irreducible representations of complex semisimple Lie groups

Developed spectral analysis methods for representations

Authored influential book on compact Lie groups

Abstract

This is a brief overview of researches of Dmitry Petrovich Zhelobenko (1934--2006). He is the best known for his book "Compact Lie groups and their representations" and for the classification of all irreducible representations of complex semisimple Lie groups. We tell also on other his works, especially on the spectral analysis of representations.