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Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$ (1902.10794v1)
Published 27 Feb 2019 in math.QA
Abstract: 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.