  We found new identities among the Dedekind eta-function, the characters of
the W_{m} algebra and those of the level 1 affine Lie algebra su(m)_{1}. They
allow to characterize the Z_{m}-orbifold of the m-component free bosons
u(1)_{K_{m,p}} (our theory TM) as an extension of the fully degenerate
representations of W_{1+infty}^{(m)}. In particular, TM is proven to be a Gamma
_{theta}-RCFT extension of the chiral fully degenerate W_{1+infty}^{(m)}.
