English

The hyperoctahedral quantum group

Representation Theory 2019-02-27 v2

Abstract

We consider the hypercube in Rn\mathbb R^n, and show that its quantum symmetry group is a qq-deformation of OnO_n at q=1q=-1. Then we consider the graph formed by nn segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted Hn+H_n^+, enlarges Wang's series Sn+,On+,Un+S_n^+,O_n^+,U_n^+.

Keywords

Cite

@article{arxiv.math/0701859,
  title  = {The hyperoctahedral quantum group},
  author = {Teodor Banica and Julien Bichon and Benoit Collins},
  journal= {arXiv preprint arXiv:math/0701859},
  year   = {2019}
}

Comments

32 pages