ar X iv : h ep - t h / 94 07 19 5 v 2 4 M ay 1 99 5 The Euclidean Hopf Algebra U q ( e N ) and its fundamental Hilbert space representations
نویسنده
چکیده
We construct the Euclidean Hopf algebra Uq(e ) dual of Fun(Rq >⊳SOq−1(N)) by realizing it as a subalgebra of the differential algebra Diff(Rq ) on the quantum Euclidean space Rq ; in fact, we extend our previous realization [1] of Uq−1(so(N)) within Diff(R N q ) through the introduction of q-derivatives as generators of q-translations. The fundamental Hilbert space representations of Uq(e N ) turn out to be of highest weight type and rather simple “ lattice-regularized ” versions of the classical ones. The vectors of a basis of the singlet (i.e. zero-spin) irrep can be realized as normalizable functions on Rq , going to distributions in the limit q → 1. 1 Alexander von Humboldt-Stiftung fellow
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