Auxiliary representations of Lie algebras and the BRST constructions
  The method of construction of auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be non -- hermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proven for any Lie algebra. 
C. Burdik, A. Pashnev and M. Tsulaia