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

## TL;DR

This paper constructs quasi-particle bases for principal subspaces of certain affine Lie algebra modules in types D, E, and F, leading to new character formulas and combinatorial identities.

## Contribution

It generalizes Georgiev's approach to types D, E, and F, providing explicit bases, presentations, and character formulas for these principal subspaces.

## Key findings

- Constructed quasi-particle bases for principal subspaces
- Derived presentations and character formulas
- Discovered new combinatorial identities

## 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.