On projective representations of finite Abelian groups

Abstract

This paper presents a complete description of a simple procedure of obtaining explicitly all the inequivalent irreducible projective matrix representations of a finite Abelian group using elementary number theory and the theory of representations of generalized Cl1Uord algebras studied extensively at MATSCIENCE by Ramakrishnan and collaborators [1 4]. I have great pleasure in dedicating this paper to Professor Paul Erdos since it was his visit to MATSCIENCE in 1975 that made me take much interest in the number theoretical aspects of physical phenomena. Projective representations of finite Abelian groups and their number theoretical aspects play particularly important roles in the dynamics of Bloch electrons in external homogeneous magnetic fields (cr., e.g., [5]). Let { eiii:: 1,2, ... ) 1'\. 1 be the generators of a finite Abelian group en Zm x ... X Zm so that any ,e G can be represented as 1 11.