The Askey–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→1 this algebra becomes the coordinate ring of a certain subalgebra of a quantum object that we call quantum cusped character variety.