q‐difference intertwining operators for a Lorentz quantum algebra

Representations π̂ r,r̄ of a Lorentz quantum algebra U are constructed. They are labeled by two complex numbers r,r̄ and act in the space of formal power series of two noncommuting variables η,η̄. These variables are built from elements of the matrix Lorentz quantum group L which is dual to U. The c...

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Bibliographic Details
Published in:Journal of mathematical physics 1994-02, Vol.35 (2), p.971-985
Main Authors: Da̧browski, L., Dobrev, V. K., Floreanini, R.
Format: Article
Language:English
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Summary:Representations π̂ r,r̄ of a Lorentz quantum algebra U are constructed. They are labeled by two complex numbers r,r̄ and act in the space of formal power series of two noncommuting variables η,η̄. These variables are built from elements of the matrix Lorentz quantum group L which is dual to U. The conditions for reducibility of π̂ r,r̄ are given. q‐difference intertwining operators in η, η̄, which realize partial equivalences of the representations π̂ r,r̄ , are constructed explicitly. The whole construction is a generalization of a known procedure for q=1. The case when q is a root of unity is also considered in detail.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.530624