  In this note, we initiate a study on Jarn\'ik-Besicovitch type theorems for
semisimple algebraic groups from the representation-theoretic point of view.
Let $\rho:\mathbf G\to\operatorname{\mathbf{GL}}(V)$ be an irreducible $\mathbb
Q$-rational representation of a connected semisimple $\mathbb Q$-algebraic
group $\mathbf G$ on a complex vector space $V$ and $\{a_t\}_{t\in\mathbb R}$ a
one-parameter subgroup in a $\mathbb Q$-split torus in $\mathbf G$. We define a
subset $S_\tau(\rho,\{a_t\}_{t\in\mathbb R})$ of Diophantine elements of type
$\tau$ in $\mathbf G(\mathbb R)$ in terms of the representation $\rho$ and the
subgroup $\{a_t\}_{t\in\mathbb R}$, and prove formulas for the Hausdorff
dimension of the complement of $S_{\tau}(\rho,\{a_t\}_{t\in\mathbb R})$. As
corollaries, we deduce several Jarn\'ik-Besicovitch type theorems.
