(k,r)-Admissible Configurations and Intertwining Operators

摘要

Certain combinatorial bases of Feigin-Stoyanovsky's type subspaces of level k standard modules for affine Lie algebra sI(r,C)~ are parametrized by (fc,r)-admissible configurations In this note we use Capparelli-Lepowsky-Milas' method to give a new proof of linear independence of these bases, the main ingredient in the proof being the use of Dong-Lepowsky's intertwining operators for fundamental s((r, C)~-modules.