  In this paper we examine fermionic type characters (Universal Chiral
Partition Functions) for general 2D conformal field theories with a bilinear
form given by a matrix of the form K \oplus K^{-1}. We provide various
techniques for determining these K-matrices, and apply these to a variety of
examples including (higher level) WZW and coset conformal field theories.
Applications of our results to fractional quantum Hall systems and (level
restricted) Kostka polynomials are discussed.
