Commutators in a Semi-Simple Lie Group

On Commutators in a Simple Lie Algebra1

Commutators associated with Schrödinger operators on the nilpotent Lie group

Assume that G is a nilpotent Lie group. Denote by [Formula: see text] the Schrödinger operator on G, where Δ is the sub-Laplacian, the nonnegative potential W belongs to the reverse Hölder class [Formula: see text] for some [Formula: see text] and D is the dimension at infinity of G. Let [Formula: see text] be the Riesz transform associated with L. In this paper we obtain some estimates for the...

Representations of Complex Semi-simple Lie Groups and Lie Algebras

This article is an exposition of the 1967 paper by Parthasarathy, Ranga Rao, and Varadarajan, on irreducible admissible Harish-Chandra modules over complex semisimple Lie groups and Lie algebras. It was written in Winter 2012 to be part of a special collection organized to mark 10 years and 25 volumes of the series Texts and Readings in Mathematics (TRIM). Each article in this collection is int...

Semi-simple Lie Algebras and Their Representations

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie algebras and Lie groups to more abstract characterizations of Lie groups, give basic definitions of different properties that may characterize Lie groups, and then prove results about root systems, pr...

Semi-Simple Lie Algebras and Their Representations