An extended trace formula for vertex operators

We present an extension of the trace of a vertex operator and explain a representation-theoretic interpretation of the trace. Specifically, we consider a twist of the vertex operator with infinitely many Casimir operators and compute its trace as a character formula. To do this, we define the Fock s...

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Bibliographic Details
Published in:Linear algebra and its applications 2023-03, Vol.661, p.1-19
Main Authors: Reza-Rahmati, Mohammad, Flores, Gerardo
Format: Article
Language:English
Subjects:
Character formula
Fock space
Infinite dimensional Lie algebras
Infinite wedge representation
Vertex operator
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Summary:We present an extension of the trace of a vertex operator and explain a representation-theoretic interpretation of the trace. Specifically, we consider a twist of the vertex operator with infinitely many Casimir operators and compute its trace as a character formula. To do this, we define the Fock space of infinite level F∞. Then, we prove a duality between gl∞ and a∞=glˆ∞ of Howe type, which provides a decomposition of F∞ into irreducible representations with joint highest weight vector for gl∞ and a∞. The decomposition of the Fock space F∞ into highest weight representations provides a method to calculate and interpret the extended trace.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2022.12.001