Hecke algebras of type An and subfactors.

摘要: In his paper [J-l] V. Jones introduced an index, which 'measures' the size of a subfactor in II1 factor. The main result that is index has to be either greater or equal than 4 it 4cosZ(x//) for some l~N, I>3 and there exist subfactors all these values. Similarly as subgroups, alone does not characterize up conjugacy by automorphisms. fact are only countably many possible values < seems related another invariant. Subfactors with less always have trivial centralizers, (or relative commutants), i.e. elements factor commute every element multiples identity. On other hand, examples given I-J-l] nontrivial centralizers. Furthermore, known commutants algebraic integer. At current state knowledge, still unknown whether Note however, set centralizer arbitrary II~ closed subset R (see [HW]). Our original motivation this was study how hyperfinite can constructed via AF algebras. We provide method computing we give upper bound subfactor. general results will then applied series complex Hecke algebras H,(q), n~N type A,_I. Their standard generators gx, g2, -.., gn1 satisfy same relations simple reflections symmetric group S, except reflection property g~ = 1 replaced g ~ ( q ) i + . It well-known H,(q) isomorphic C S , if root unity. If parameter unity, Hn(q) may no longer bc sernisimple its structure general. This is, most interesting case far concerned. define representations p Ha(q) such p(H,(q)) semisimple n~N. Together