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Posted 2022-08-12Updated 2022-08-12Algebra / Representation Theory / Linear Algebra / Finite Groups / Finite Fields

Irreducible 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.
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Posted 2022-06-16Updated 2022-12-19Algebra / Representation Theory / Linear Algebra / Lie Groups

Irreducible 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.
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Posted 2022-05-08Updated 2022-07-26Analysis / Algebra / Representation Theory / Linear Algebra / Fourier Series / Lie Groups

Study 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.
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Posted 2022-01-18Updated 2022-01-24Algebra / Representation Theory / Group Algebra / Non-Commutative Ring

The 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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Desvl

Desvl

A blog mainly on graduate mathematics.

A Noetherian local ring

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