Vertex operator construction of standard modules for A_n⁽¹⁾

Mirko Primc

Vol. 162 (1994), No. 1, 143–187

DOI: 10.2140/pjm.1994.162.143

Abstract

We generalize the vertex operator formula for the affine Lie algebra A_n⁽¹⁾ in the “homogeneous picture” and by using it we construct a basis of any given standard A_n⁽¹⁾-module parametrized by coloured partitions. We also obtain a similar explicit construction of vacuum spaces of standard A₂⁽¹⁾-modules.

Mathematical Subject Classification 2000

Primary: 17B67

Milestones

Received: 10 August 1990

Revised: 1 July 1991

Published: 1 January 1994