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Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras. (English) Zbl 0877.33013

The authors present a one-parameter family of constant solutions of the reflection equation, define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group and then identify the zonal spherical functions as multivariable Askey-Wilson polynomials containing two continuous and two discrete parameters.

MSC:

33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
17B37 Quantum groups (quantized enveloping algebras) and related deformations
33D60 Basic hypergeometric integrals and functions defined by them
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