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- W2950265506 abstract "Eigenfunctions of the Askey-Wilson second order $q$-difference operator for $0<q<1$ and $|q|=1$ are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra $U_q(sl(2,mathbb{C}))$. The eigenfunctions are in integral form and may be viewed as analogues of Euler's integral representation for Gauss' hypergeometric series. We show that for $0<q<1$ the resulting eigenfunction can be rewritten as a very-well-poised ${}_8phi_7$-series, and reduces for special parameter values to a natural elliptic analogue of the cosine kernel." @default.
- W2950265506 created "2019-06-27" @default.
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- W2950265506 date "2003-01-28" @default.
- W2950265506 modified "2023-09-23" @default.
- W2950265506 title "Askey-Wilson functions and quantum groups" @default.
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