Nonstandard q-deformation of the Euclidean Lie algebra and its representations

A nonstandard g-deformed Euclidean algebra U-q(iso(n)), based on the defini tion of the twisted q-deformed algebra U-q'(so(n)) (different from the Drin feld-Jimbo algebra. U-q(so(n))), is defined. Infinite dimensional represent ations R of U-q(iso(n)) are described. Explicit formulas for operators of t hese representations in the orthonormal basis are given. The spectra of the operators R(T-n) corresponding to a q-analogue of the infinitesimal operat or of shifts along the n-th axis are described. Contrary to the case of the classical Euclidean Lie algebra iso(n), these spectra are discrete and spe ctral points have one point of accumulation.