Automorphisms of DAHA type check C1 C1 map Askey-Wilson polynomials to functions and produce a symmetric plus anti-symmetric expression for the non-symmetric Askey-Wilson function.
Mazzocco, Confluences of the Painlev´ e equations, Cherednik algebras and q-Askey scheme, Nonlinearity 29 (2016), 2565–2608
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Automorphisms of the DAHA of type $\check{C_1}C_1$ and non-symmetric Askey-Wilson functions
Automorphisms of DAHA type check C1 C1 map Askey-Wilson polynomials to functions and produce a symmetric plus anti-symmetric expression for the non-symmetric Askey-Wilson function.