2003/01/28 by Jasper V. Stokman, Stokman, Jasper V.
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CA #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0301330
25 pages
arxiv created 2003/01/28 · arxiv updated 2009/11/30
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 Uq(sl(2,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 8ϕ7-series, and reduces for special parameter values to a natural elliptic analogue of the cosine kernel.