Abstract
We present a general survey of some recent developments regarding the construction of compact quantum symmetric spaces and the analysis of their zonal spherical functions in terms of q-orthogonal polynomials. In particular, we define a one-parameter family of two-sided coideals in U q(gι(n, ℂ)) and express the zonal spherical functions on the corresponding quantum projective spaces as Askey-Wilson polynomials containing two continuous and one discrete parameter.
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