  In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the
GL(m|n) type quantum matrix algebra was obtained. Here we continue
investigation of that identity. We derive it in three alternative forms and,
most importantly, we obtain it in a factorized form. The factorization leads to
a separation of the spectra of the quantum supermatrix into the "even" and
"odd" parts. The latter, in turn, allows us to parameterize the characteristic
subalgebra (which can also be called the subalgebra of spectral invariants) in
terms of the supersymmetric polynomials in the eigenvalues of the quantum
supermatrix. For our derivation we use two auxiliary results which may be of
independent interest. First, we calculate the multiplication rule for the
linear basis of the Schur functions $s_{\lambda}(M)$ for the characteristic
subalgebra of the Hecke type quantum matrix algebra. The structure constants in
this basis are the Littlewood-Richardson coefficients. Second, we derive a
series of bilinear relations in the graded ring $\Lambda$ of Schur symmetric
functions in countably many variables.
