Multi-Sided Braid Type Subfactors, II

[摘要] We show that the multi-sided inclusion $R^{otimes l} subset R$ ofbraid-type subfactors of the hyperfinite II$_1$ factor $R$, introducedin {it Multi-sided braid type subfactors} [E3], contains a sequenceof intermediate subfactors: $R^{otimes l} subset R^{otimes l-1}subset cdots subset R^{otimes 2} subset R$. That is, every$t$-sided subfactor is an intermediate subfactor for the inclusion$R^{otimes l} subset R$, for $2leq tleq l$. Moreover, we alsoshow that if $t>m$ then $R^{otimes t} subset R^{otimes m}$ isconjugate to $R^{otimes t-m+1} subset R$. Thus, if the braidrepresentation considered is associated to one of the classical Liealgebras then the asymptotic inclusions for the Jones-Wenzl subfactorsare intermediate subfactors.

[学科分类] 数学（综合）

[关键词] linear map;unitary group;general linear group