In this paper linear representations of finite groups are introduced, and the associated character theory with it. Some work of linear representations of the dihedral group $D_n$ and the symmetric group $S_n$ is presented. \\We also take a look at the finite matrix groups $\textbf{GL}(\mathbb{F}_q)$ and $\textbf{SL}(\mathbb{F}_q)$. The character table for $\textbf{SL}(\mathbb{F}_4)$ and its representation spaces in an implicit form are calculated. We define the standard representation $\varphi $ of $\textbf{SL}(\mathbb{F}_q)$ and prove that it is irreducible for an arbitrary finite field $\mathbb{F}_q$.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-315364 |
| Date | January 2022 |
| Creators | Mevik Päts, Oskar |
| Publisher | KTH, Fysik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | TRITA-SCI-GRU ; 2022:116 |
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