  We show that the Eigenspace Representations for $\mathbb{R}^{n}$ semidirect
with a finite pseudo-reflection group $K$, which satisfy some generic property
are equivalent to the induced representations from $\mathbb{R}^{n}$ to
$\mathbb{R}^{n} \rtimes K$, which satisfy the same property by Mackey little
group method.And the proof of the equivalence is by using matrix coefficients
and invariant theory.As a consequence, these eigenspace representations are
irreducible.
