Character generators for elements of finite order in simple Lie groups A1, A2, A3, B2, and G2

Abstract

Elements of finite order in the compact simple Lie groups SU(2), SU(3), SU(4), Sp(4) or O(5), and G(2) are considered. We provide the characters of the elements on irreducible representations of Lie groups by assigning appro- priate numerical values to the variables on which the characters of representations of the Lie group depend. In this way we specialize generating functions for the characters of the representations of the Lie groups to the generating functions for characters of the elements of finite order. Particular attention is paid to rational elements, all of whose characters are integers; they are listed and the generating functions for their characters are obtained in a simplified form from which the characters can be read. Gaussian elements are also studied in detail. Their characters are complex valued with integer real and imaginary parts.