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Representation theory approach to the polynomial solutions of <i>q</i>-difference equations: U<i>q</i>(sl(3)) and beyond
A new approach to the theory of polynomial solutions of q-difference equations is proposed. The approach is based on the representation theory of simple Lie algebras 𝒢 and their q-deformations and is presented here for Uq(sl(n)). First a q-difference realization of Uq(sl(n)) in terms of n(n−1)/2 commuting variables and depending …