Spectra and Eigenfunctions of Representation Operators for Quantum Groups and q-Oscillators

Properties of operators of irreducible representations of quantum algebras (q-deformed universal enveloping algebras of Lie algebras) very often differ from these of representation operators for Lie algebras. The main differences are: (a)discrete spectra of operators of representations of finite dimensional representations are mostly non-equidistant(b)closures of unbounded symmetric operators of representations of infinite dimensional irreducible representations are not mostly selfadjoint (in these cases, they have equal deficiency indices and therefore we can construct their selfadjoint extensions)