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

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.

35 pages

References in corpus (3)

• Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$
• Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
• Lift of dilogarithm to partition identities

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