WZNW Models from Non-Standard Bilinear Forms

We study the WZNW models based on nonstandard bilinear forms. We approach the problem from algebraic, perturbative and functional exact methods. It is shown that even in the case of integer $k$ we can find irrational CFT's. We prove that when the base group is noncompact with nonabelian maximal compact subgroup, the Kac-Moody representations are nonunitary.