On subfactors arising from asymptotic representations of symmetric groups

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial representation of the larger group. We compute subfactor invariants of this construction in terms of the Thoma parameter.Comment: to appear in Proc. AM

A few remarks on the tube algebra of a monoidal category

We prove two results on the tube algebras of rigid C$^*$-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group $G$ is a full corner of the Drinfeld double of $G$. As an application we obtain some information on the structure of the tube algebras of the Temperley-Lieb categories $TL(d)$ for $d>2$. The second result is that the tube algebras of weakly Morita equivalent C$^*$-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the $2$-category defining the Morita context.Comment: 17 pages; v4: minor changes and change of section numbering to the published version, to appear in Proc. Edinb. Math. Soc.; v3: description of the topology on the primitive spectrum of the tube algebra of a Temperley-Lieb category (d>2), a few remarks and minor fixes; v2: rewritten last sectio