Vector Generation Functions, q-Spectral Functions of Hyperbolic Geometry and Vertex Operators for Quantum Affine Algebras

TL;DR

This paper explores the connection between q-replicated arguments in symmetric functions, spectral functions of hyperbolic geometry, and their applications in vector generation functions and string theory, aiming to bridge mathematics and physics.

Contribution

It introduces a novel approach linking q-replicated arguments with spectral functions, enriching the mathematical framework with insights from physics.

Findings

Established a connection between q-replicated arguments and spectral functions.

Developed vector generation functions using q-series.

Suggested potential applications in string theory.

Abstract

We investigate the concept of $q$-replicated arguments in symmetric functions with its connection to spectral functions of hyperbolic geometry. This construction suffices for vector generation functions in the form of $q$-series, and string theory. We hope that the mathematical side of the construction can be enriched by ideas coming from physics.