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The Hyperoctahedral Quantum Group
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We consider the hypercube in Rn, and show that its quantum symmetry group is a q-deformation of On at q = −1. Then we consider the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted H+n , enlarges Wang’s series S+n , O+n , U+n.
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