Corpus ID: 119304489

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

@article{Butorac2019PrincipalSF,
  title={Principal subspaces for the affine Lie algebras in types \$D\$, \$E\$ and \$F\$},
  author={Marijana Butorac and Slaven Kovzi'c},
  journal={arXiv: Quantum Algebra},
  year={2019}
}
We consider the principal subspaces of certain level $k\geqslant 1$ 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. 
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