The hyperoctahedral quantum group

Details The hyperoctahedral quantum group The hyperoctahedral quantum group

2007-01-29

arxiv.org/abs/math/0701859v2

J. Ramanujan Math. Soc. 22 (2007), 345-384

Mathematics

Representation Theory

32 pages

Scientific paper

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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