Exercise 1, § 4

Let $E^0$ be the orthogonal complement of $E$ with respect to the form $B_M$. Show that $E^0$ is the radical of the $W$-module $E$ (\emph{Algebra}, Chap. VIII, § 6, no. 2), and that $E/E^0$ is the direct sum of $m$ absolutely simple, pairwise non-isomorphic modules, where $m$ is the number of connected components of the graph of $S$.