  The Green ring of the half quantum group $H=U_n(q)$ is computed in [Chen, Van
Oystaeyen, Zhang]. The tensor product formulas between indecomposables may be
used for a generalized subgroup depth computation in the setting of quantum
groups -- to compute depth of the Hopf subalgebra $H$ in its Drinfeld double
$D(H)$. In this paper the Hopf subalgebra quotient module $Q$ (a generalization
of the permutation module of cosets for a group extension) is computed and, as
$H$-modules, $Q$ and its second tensor power are decomposed into a direct sum
of indecomposables. We note that the least power $n$, referred to as depth, for
which $Q^{\otimes (n)}$ has the same indecomposable constituents as $Q^{\otimes
(n+1)}$ is $n = 2$, since $ Q^{\otimes (2)}$ contains all $H$-module
indecomposables, which determines the minimum even depth $d_{ev}(H,D(H)) = 6$.

Representation Theory