Tridiagonal representations of the q-oscillator algebra and Askey-Wilson polynomials
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
TL;DR
This paper constructs the most general tridiagonal representations of the q-oscillator algebra and links them to Askey-Wilson polynomials, advancing the understanding of their algebraic and polynomial structures.
Contribution
It introduces the broadest class of tridiagonal representations of the q-oscillator algebra and establishes their connection to Askey-Wilson polynomials.
Findings
Connected tridiagonal q-oscillator representations to Askey-Wilson polynomials.
Provided a comprehensive construction of these algebra representations.
Enhanced the algebraic understanding of Askey-Wilson polynomials.
Abstract
A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey-Wilson polynomials.
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