The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups asso

Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems

This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description

Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable

This work is intended for graduate students and research mathematicians interested in topological groups, Lie groups, and harmonic analysis.