RT6. Representations on Function Spaces 
RT6. Representations on Function Spaces
by Robert Donley
Video Lecture 8 of 18
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Date Added: March 14, 2015

Lecture Description

Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in several ways. We give an overview of features to expect from Fourier analysis on the circle group.

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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