Higher orbitals of quizzy quantum group actions

Abstract

The hyperoctahedral group H N is known to have two natural liberations: the "good" one H + N , which is the quantum symmetry group of N segments, and the "bad" oneŌ N , which is the quantum symmetry group of the N -hypercube. We study here this phenomenon, in the general "quizzy" framework, which covers the various liberations and twists of H N , O N . Our results include: (1) an interpretation of the embeddinḡ O N ⊂ S + 2 N , as corresponding to the antisymmetric representation of O N , (2) a study of the liberations of H N , notably with the result < H + N ,Ō N >= O + N , and (3) a comparison of the k-orbitals for the inclusions H N ⊂ H + N and H N ⊂Ō N , for k ∈ N small.2010 Mathematics Subject Classification. 46L65 (46L54).

Modelling questions for transitive quantum groups

“…By performing some standard manipulations, these quantities χ r correspond to the various antisymmetric representations of O n , and this leads to the result. See [7]. Now back to our modelling questions, we know that the flat model space for O −1 n appears by imposing the conditions from Proposition 7.6 above.…”

“…, where I n is the graph formed by n segments, having N = 2n vertices. (7) Once again this comes from a result from [12], stating that we have…”

“…In the case where ∼ k with k ≥ 3 happens to be transitive, and so is an equivalence relation, we can call its equivalence classes the algebraic k-orbitals of G. See [7].…”

“…In addition, we believe that in the case where E is easy these examples should be covered by a suitable projective extension of the twisting procedure in [7].…”

A state-space approach to quantum permutations

“…. , (k 18 , k 27 ), namely alternating (3,3) and (1, 1), except for (k 14 , k 23 ) = (2,4). This leaves: which is strictly positive.…”