Howe duality and algebras of the Askey-Wilson type: an overview
Julien Gaboriaud, Luc Vinet, St\'ephane Vinet
TL;DR
This paper surveys the role of Howe duality in the structure of Askey-Wilson and related algebras, highlighting their connections to orthogonal polynomials and their presentations as commutants.
Contribution
It provides an overview of how Howe duality underpins the algebraic structures of Askey-Wilson and related algebras, linking them to orthogonal polynomials.
Findings
Askey-Wilson algebra relates to orthogonal polynomials.
These algebras can be presented as commutants via Howe duality.
The survey connects algebraic structures with duality principles.
Abstract
The Askey-Wilson algebra and its relatives such as the Racah and Bannai-Ito algebras were initially introduced in connection with the eponym orthogonal polynomials. They have since proved ubiquitous. In particular they admit presentations as commutants that are related through Howe duality. This paper surveys these results.
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