RT7.1: Finite Abelian Groups: Character Orthogonality 
RT7.1: Finite Abelian Groups: Character Orthogonality
by Robert Donley
Video Lecture 9 of 18
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Date Added: March 14, 2015

Lecture Description

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.

Course materials, including problem sets and solutions, available at mathdoctorbob.org/UR-RepTheory.html

Course Index

Course Description

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.

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