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

Abstract

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.

24 pages, 1 figure, comments are welcome

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Cited by in corpus (3)

• Some remarks on associated varieties of vertex operator superalgebras
• Combinatorial bases of standard modules of twisted affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$: rectangular highest weights
• Principal subspaces for the quantum affine vertex algebra in type $A_1^{(1)}$