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The Groenewold-Moyal plane is the algebra A_\theta(R^(d+1)) of functions onR^(d+1) with the star-product as the multiplication law, and the commutator[x_\mu,x_\nu] =i \theta_{\mu \nu} between the coordinate functions. Chaichianet al. and Aschieri et al. have proved that the Poincare group acts asautomorphisms on A_\theta(R^(d+1))$ if the coproduct is deformed. (See also theprior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism groupwith a deformed coproduct also does so according to the results of Aschieri etal. In this paper we show that for this new action, the Bose and Fermicommutation relations are deformed as well. Their potential applications to thequantum Hall effect are pointed out. Very striking consequences of thesedeformations are the occurrence of Pauli-forbidden energy levels andtransitions. Such new effects are discussed in simple cases.Comment: 18 pages, LaTex. References added and typos correcte

SPIN AND STATISTICS ON THE GROENEWOLD–MOYAL PLANE: PAULI-FORBIDDEN LEVELS AND TRANSITIONS