RT8.2. Finite Groups: Classification of Irreducibles 
RT8.2. Finite Groups: Classification of Irreducibles
by Robert Donley
Video Lecture 13 of 18
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Date Added: March 14, 2015

Lecture Description

Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) using irreducible characters, and from this we see that the number of irreducible classes equals the number of conjugacy classes in G. We also obtain character formulas for multiplicities.

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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