engleski

Principal subspaces for the affine Lie algebras in types D, E and F

We consider the principal subspaces of certain level k>=1 integrable highest weight modules and generalized Verma modules for the untwisted affine Lie algebras in types D, E and F. Generalizing the approach of G. Georgiev we construct their quasi-particle bases. We use the bases to derive presentations of the principal subspaces, calculate their character formulae and find some new combinatorial identities.

Principal subspaces ; Combinatorial bases ; Combinatorial identities ; Quasi-particles ; Vertex operator algebras ; Affine Lie algebras

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