Multi-Sided Braid Type Subfactors, II

Erlijman, Juliana

Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 80-94

Résumé

We show that the multi-sided inclusion ${{R}^{\otimes l}}\,\subset \,R$ of braid-type subfactors of the hyperfinite $\text{I}{{\text{I}}_{1}}$ factor $R$ , introduced in Multi-sided braid type subfactors $[\text{E}3]$ , contains a sequence of 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 ${{R}^{\otimes l}}\,\subset \,R,\,\text{for 2}\,\le \,t\,\le \,l$ . Moreover, we also show that if $t\,>\,m$ then ${{R}^{\otimes t}}\,\subset \,{{R}^{\otimes m}}$ is conjugate to ${{R}^{\otimes t-m+1\,}}\subset \,R$ . Thus, if the braid representation considered is associated to one of the classical Lie algebras then the asymptotic inclusions for the Jones-Wenzl subfactors are intermediate subfactors.

Détail

DOI : 10.4153/CMB-2003-008-7

Mots-clés : 46L37