\[Z_{\kappa}\left(\mathbf{T}\right)=Z_{\kappa}\left(\mathbf{I}\right)\,\left|%
\mathbf{T}\right|^{k_{m}}\*\int\limits_{\mathbf{O}(m)}\prod_{j=1}^{m-1}|(%
\mathbf{H}\mathbf{T}\mathbf{H}^{-1})_{j}|^{k_{j}-k_{j+1}}\mathrm{d}{\mathbf{H}},\]