Analysis on the 2-Dim Quantum Poincare` Group at Roots of Unity
Abstract
2-Dim quantum Poincare` Group Eq(1,1) at roots of unity, its dual Uq(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on Eq(1,1) and its invariant discrete subgroup E(1,1 p) are constructed. *-Representations of the quantum algebra Uq(e(1,1)) constructed in the homogeneous space SO(1,1 p) are integrated to the pseudo-unitary representations of Eq(1,1) by means of the universal T-matrix. Uq(e(1,1)) is realized on the quantum plane Eq(1,1) and the eigenfunctions of the complete set of observables are obtained in the angular momentum and momentum basis. The matrix elements of the pseudo-unitary irreducible representations are given in terms of the cut off q-exponential and q-Bessel functions whose properties we also investigate.
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