Artin's Theorem of Induced Characters

We give a relatively more detailed proof of Artin's theorem in representation theory of finite groups as well as an example of dihedral group.

Read moreArtin's Theorem of Induced Characters

We give a relatively more detailed proof of Artin's theorem in representation theory of finite groups as well as an example of dihedral group.

Read moreProjective Representations of SO(3)

In this post we study projective representations of $SO(3)$, although we will make more use of $SU(2)$. At the end of this post we reach the conclusion that one will think about polynomials with odd or even terms. Projective representations have its own significance in physics although the room of this post is too small to contain it. Nevertheless, the reader is invited to use linear algebra much more extensively with a taste of modern physics in this post.

Read moreIrreducible Representations of GL_2(F_q)

In this post we follow the step of Fulton-Harris to classify all irreducible representations of $GL_2(\mathbb{F}_q)$. A character table is added at the end.

Read moreIrreducible Representations of SO(3) and the Laplacian

In this post, irreducible representations of $SO(3)$ are studied, with much more extensive applications of linear algebra.

Read moreStudy Irreducible Representations of SU(2) Using Fourier Series

$SU(2)$ has a lot of interesting mathematical and physical properties. In this post we study its irreducible representations in a mathematician's way.

Read moreThe Group Algebra of A Finite Group and Maschke's Theorem

In this post we give several forms of Masher's theorem by studying group algebra, which eventually becomes a study of semisimple rings. One can consider this post a chaotic evil introduction to representation theory or something.

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