I'm planning to explain several applications of a Fermionic Formula for parabolic Kostka polynomials discovered by the author of this talk in 1982/83, to give proofs of a number of conjectures (and their generalization) in Cpmbinatorics and Representation Theory (for type A ) concerning q-Kostka polynomials, such as the Gupta--Brylinski , Generalized Saturation, Combinatorial Unimodality, Polynomiality Conjectures, and new interpretation of Littlewood--Richardson and Kronecker numbers.