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Description

The Askeyâ Wilson polynomials are a special case of Macdonald polynomials; their degenerations are organised into a hierarchy called $q$-Askey scheme. In this talk the speaker will give a new approach to study degenerations as well as dualities in the $q$-Askey scheme, based on the fact that all families of polynomials in the $q$-Askey scheme admit a certain algebra of symmetries (the Zhedanov algebra and its degenerations) and in the limit as $q\to 1$ this algebra becomes the coordinate ring of a certain subalgebra of a quantum object that we call quantum cusped character variety.