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I'm looking for references for the following statements, which I believe are true: Let $G$ be a simply connected simple linear algebraic group over a finite field $k$ of cardinality $q\ge 4$. Let $Z\...

Let $\mathbb{G}$ be a connected reductive $\mathbb{F}_q$ algebraic group over its algebraic closure $\bar{\mathbb{F}_q}$, and $\mathbb{T}$ be an $\mathbb{F}_q$-defined maximal torus. Let $\Phi$ be the ...

Let $P_{\alpha}$ be the principal series representation of $GL_n(\mathbb{F}_q)$, where $\alpha = ( \alpha_1, \alpha_2, \cdots, \alpha_n)$ and $\alpha_i : \mathbb{F}_q^* \rightarrow \mathbb{C}^*$. ...

Let $\newcommand{\dbF}{\mathbb F}\dbF_q$ be a finite field and let $G\subseteq\mathrm{GL}_N(\bar{\dbF}_q)$ be a connected reductive group defined over $\dbF_q$. Let $F$ be the associated Frobenius map,...

The question is related to this post Representation theory of the general linear group over a finite prime field However, I am asking for more detailed references for n small, for example, for n=2, ...