I am looking for an explicit description of the finite dimensional irreducible representations of the classical Lie group $\text{Sp}(2) = \{A\in M_2(\mathbb{H})\,|\,A\overline{A}^T = I\}$.
I can easily find the above info for orthogonal groups and unitary groups (the representations coming from certain spaces of harmonic polynomials) but cannot seem to find such a description for the groups $\text{Sp}(n)$.
In particular I am aware that the irreducible representations of $\text{Sp}(2)$ are classified by Young diagram parameters $(a,b)$ with $a\geq b \geq 0$ but I would like to compute with such spaces so need an explicit description if possible.