On the Fock representation of the q-commutation relations
Ken Dykema, Alexandru Nica
Abstract
The q-commutation relations in the title are those that have recently received much attention, and that for -1<q<1 provide an interpolation between Bosonic and Fermionic statistics, passing through free statistics at q=0. We look at the C*-algebra Rq generated by the representation of these relations on the twisted Fock space of Bozejko-Speicher, and we find a canonical unitary Uq from the twisted Fock space to usual full Fock space, such that Uq Rq (Uq)* contains the Cuntz algebra R0, and such that we have equality for |q|<0.44.
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