Semi-Infinite Wedges and Vertex Operators

Abstract

The level 1 highest weight modules of the quantum affine algebra $U_q({\widehat{\mathfrak{sl}}}_n)$ can be described as spaces of certain semi-infinite wedges. Using a $q$-antisymmetrization procedure, these semi-infinite wedges can be realized inside an infinite tensor product of evaluation modules. This realization gives rise to simple descriptions of vertex operators and (up to a scalar function) their compositions.

17 pages