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The hyperoctahedral quantum group

Teodor Banica·Julien Bichon·Benoit Collins
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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 $S_n^+,O_n^+,U_n^+$.

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Teodor Banica, Julien Bichon, Benoit Collins. 2007-01-29. The hyperoctahedral quantum group. https://arxiv.org/abs/math/0701859

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