Symmetry Studies

Abstract

In this seminar I will outline the theory and methods of symmetry studies, including the notions of structured data and data reduction by symmetrically equivalent components. I will briefly review the elements of linear representation of finite groups and show their relation to Fisher-Cochran's theory of probability distributions for quadratic forms- This is the Canonical Decomposition theorem. This relationship will be introduced within the context of simplifying a simple data structure used in molecular biology. I will also briefly touch on the techniques of spectral analysis for data indexed by a finite group and on data structures induced by point groups from classical chemistry.