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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Product decomposition for intersection of a parabolic with a mirabolic of a closed subgroup

Let $G$ be a reductive group defined over $\mathbb{Z}_{p}$ and let $H$ be a closed reductive subgroup of $G$. Let $Q_{G}$ be a parabolic subgroup of $G$ with Levi decomposition $Q_{G} = L_{G} \ltimes …