The hyperoctahedral quantum group

Abstract

We consider the hypercube in ${\mathbb{R}}^n$, and show that its quantum symmetry group is a $q$-deformation of $O_n$ 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 $S_n^{+},O_n^{+},U_n^{+}$.

32 pages

References in corpus (3)

• Integration over quantum permutation groups
• Integration over the Pauli quantum group
• Gaussian fluctuations of representations of wreath products

Cited by in corpus (37)

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