Table 2:

Irreducible representations of $𝒢\times 𝒜$

${\psi }_{k,m}((g,a))$		$m=0$	$m=1$	$\cdots$
		${\eta }_0(a)$	${\eta }_1(a)$	$\cdots$
$k=0$	${\rho }_0(g)$	${\rho }_0(g)\otimes {\eta }_0(a)$	${\rho }_0(g)\otimes {\eta }_1(a)$	$\cdots$
$k=1$	${\rho }_1(g)$	${\rho }_1(g)\otimes {\eta }_0(a)$	${\rho }_1(g)\otimes {\eta }_1(a)$	$\cdots$
$k=2$	${\rho }_2(g)$	${\rho }_2(g)\otimes {\eta }_0(a)$	${\rho }_2(g)\otimes {\eta }_1(a)$	$\cdots$
$k=3$	${\rho }_3(g)$	${\rho }_3(g)\otimes {\eta }_0(a)$	${\rho }_3(g)\otimes {\eta }_1(a)$	$\cdots$
$⋮$	$⋮$	$⋮$	$\ddots$