Quasi-particles models for the representations of Lie algebras and geometry of flag manifold

TL;DR

This paper introduces a new semi-infinite construction for integrable representations of affine Kac-Moody algebras, providing novel proofs and interpretations of quasi-particle character formulas and Gordon identities.

Contribution

It offers a new semi-infinite approach to understanding quasi-particle formulas and connects algebraic and geometric perspectives on affine Kac-Moody representations.

Findings

New semi-infinite construction of representations

Alternative proofs of quasi-particle character formulas

Connections between algebraic formulas and flag manifold geometry

Abstract

We give a new interpretation and proof of the "quasi-particle" type character formulas for integrable representations of the simply-laced affine Kac-Moody algebras through a new "semi-infinite" construction of such representations. We compare formulas of this kind to other formulas obtained using the geometry of the corresponding flag manifold and in particular give a new proof to the Gordon type identities.