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Integration over the Pauli quantum group

Authors:	Teodor Banica,Benoî t Collins

Affiliation:	1. Department of Mathematics, Paul Sabatier University, 118 route de Narbonne, 31062 Toulouse, France;2. Department of Mathematics, Claude Bernard University, 43 bd du 11 novembre 1918, 69622 Villeurbanne, France;3. University of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5, Canada

Abstract:	We prove that the Pauli representation of the quantum permutation algebra _A_s(4) $A_{s} (4)$ is faithful. This provides the second known model for a free quantum algebra. We use this model for performing some computations and show that, at the level of the laws of diagonal coordinates, the Lebesgue measure appears between the Dirac mass and the free Poisson law.

Keywords:	46L65 (46L54)
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