  We study the twist-field representations of W-algebras and generalize
construction of the corresponding vertex operators to D- and B-series. It is
shown, how the computation of characters of these representations leads to
nontrivial identities involving lattice theta-functions. We also propose a way
to calculate their exact conformal blocks, expressing them for D-series in
terms of geometric data of the corresponding Prym variety for covering curve
with involution.
