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Let $k$ be a number field and $S$ be a finite set of places of $k$. Let $G$ be a connected semisimple algebraic group over $k$. Let $k_S=\prod_{v\in S}k_v$ where $k_v$ is the completion of $k$ at $v$. …

This note appears in "Proceedings of Symposia in pure mathematics" vol.33 1979 part 1 pp. 26-69. The question will be about materials on page 31-32. Let $G$ be a reductive algebraic group (not neces …

I feel experts might be able to answer this question immediately. Let $G$ be a connected $\mathbb Q$-simple and $\mathbb Q$-isotropic algebraic group. Let $S$ be a maximal $\mathbb Q$-split torus o …

Let $G$ be a linear algebraic group defined over $\mathbb Q$. Suppose that $G$ is isomorphic to $SL_n$ over $\mathbb R$. Suppose the $\mathbb Q$-rank of $G$ is fixed, say $m$. How many types are the …

Let $G$ be a connected semisimple algebraic group defined over $\mathbb Q$. Could some expert give me a complete classification of finite dimensional $\mathbb Q$-irreducible representations of $G$? …

Let $G$ be an algebraic group defined over a char 0 local field $k$. Following Borel and Tits (73) we define the group $G^+(k)$ or $G^+$ by the subgroup of $G(k)$ generated by the unipotent elements o …

Let $G$ be a simply connected semisimple algebraic $K$-group and $K$ be a finite extension of $k$. Is $R_{K/k}G$ still a simply connected algebraic group? We say $G$ is simply connected if for any c …

Let $U$ be a unipotent upper triangluar group over a local field $K$ of characteristic zero. Can we guarantee that there is a right translation invariant metric on $U$ such that any ball of finite r …

Let $G$ be a semi-simple algebraic group defined over a global function field $K$. Let $S$ be a finite set of places of $K$. For a place $v$ of $K$ let $K_v$ be the completion under $v$. We take $K_S= …

Let $\mathfrak g$ be a real semisimple Lie algebra (without compact factors) with Iwasawa decomposition $\mathfrak g=\mathfrak k\oplus \mathfrak a\oplus \mathfrak u$. Let $\mathfrak p$ be a para …