Semi-Infinite Wedges and Vertex Operators
Eugene Stern (UC Berkeley)
TL;DR
This paper presents a new realization of level 1 highest weight modules of quantum affine algebra $U_q(\\widehat{\ rak{sl}}_n)$ as semi-infinite wedges, simplifying the description of vertex operators and their compositions.
Contribution
It introduces a $q$-antisymmetrization approach to embed semi-infinite wedges into infinite tensor products, providing clearer descriptions of vertex operators.
Findings
Realization of modules as semi-infinite wedges
Simplified descriptions of vertex operators
Explicit composition formulas for vertex operators
Abstract
The level 1 highest weight modules of the quantum affine algebra can be described as spaces of certain semi-infinite wedges. Using a -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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Matrix Theory and Algorithms · Advanced Topics in Algebra