Howe duality and algebras of the Askey-Wilson type: an overview

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.

8 pages, Proceedings for XI. International Symposium Quantum Theory and Symmetries, 1 - 5 July 2019, Montreal, Canada

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Cited by in corpus (2)

• Sklyanin-like algebras for ($q$-)linear grids and ($q$-)para-Krawtchouk polynomials
• A Howe correspondence for the algebra of the $\mathfrak{osp}(1|2)$ Clebsch-Gordan coefficients