  This monograph, along with a self-consistent presentation of the theory of
q-W-algebras including the construction of algebraic group analogues of Slodowy
slices, contains a description of q-W-algebras in terms of Zhelobenko type
operators introduced in the book. This description is applied to prove the De
Concini-Kac-Procesi conjecture on the dimensions of irreducible modules over
quantum groups at roots of unity.
