Lattice points and Lie groups. III

If a compact, simply connected, semisimple Lie group is considered as a Riemannian manifold with metric arising from the negative of the Killing form it is shown that its volume is

$${(4\pi )^{\dim G/2}}\Gamma (\dim G/2 + 1)(1/\vert w\vert)\int_{\vert\Lambda \vert \leqslant 1} {{f^{{2_{(\Lambda )d\Lambda }}}}.}$$