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Mathematics

Abstract. Using a suitably noncommutative flat matrix model, it is shown that the quantum permutation group has free orbitals: that is, a monomial in the generators of the algebra of functions can be zero for trivial reasons only. It is shown that any strictly intermediate quantum subgroup between the classical and quantum permutation groups must have free three-orbitals. This is used to give explicit formulae for the Haar state on degree four monomials that hold for such intermediate quantum subgroups as well as the quantum permutation group itself.

 

 

 

 

  • Shane O'RourkeFree actions on metric lines. Talk at Groups and their Actions 2019 conference, Politecnica Slaska, Gliwice, Poland.

 

  • Shane O'RourkeA combination theorem for affine tree-free groups. Talk at Geometric and Asymptotic Group Theory with Applications (GAGTA10) conference (Stevens Institute of Technology, New Jersey).

  • Shane O'RourkeA combination theorem for affine tree-free groups. Invited speaker at Groups in Galway annual conference (NUI Galway).
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