\(k\)-fold anti-invariant subspaces of a linear mapping. (Q1414691)

Given a nonsingular linear transformation \(\pi\) on a finite dimensional vector space, a subspace \(T\) is called \(k\)-fold anti-invariant if \[ T+T\pi +\ldots +T\pi^k =T \oplus T\pi \oplus \ldots \oplus T\pi^k. \] A necessary and sufficient condition for the maximal dimension of such subspace \(T\) is given in terms of degrees of the invariant divisors of \(\pi\).