We establish an analogue of Fourier analysis for a finite abelian group G. A decomposition of L^2(G) is given in terms of characters. Versions of Schur Orthogonality Relations and the Peter-Weyl Theorem are given.
Doctor Bob provides 18 short video lectures on the introduction to representation theory. Group representations are where group theory meets linear algebra, and important applications arise in various math subjects (number theory, analysis, algebraic geometry), physics, and chemistry.
We consider the basic representation theory of finite groups. Goals include a look at Fourier series/analysis using groups and elementary character theory.