viii CONTENT S 2.5. Inde x fo r subfactor s 1 7 2.6. Th e basic construction 1 8 2.7. Th e basic construction i n finite dimensions 1 9 2.8. Tw o basic constructions, proo f o f Goldman' s theore m 2 0 Lecture 3. Values of the Index, Virasoro Algebra 2 3 3.1. Value s of the index 2 3 3.2. Th e Virasoro unitarity resul t 2 4 3.3. Th e continuous serie s for subfactor s 2 5 3.4. Iteratin g the basic construction: th e e\ algebra 2 6 3.5. Combinatoric s o f the e/'s 2 6 3.6. Th e 67 algebra i s a Hi facto r 2 7 3.7. Th e element e\ V ei V V en, th e values 4cos 2 \ 2 8 3.8. Ghost s 3 0 Lecture 4. Constructio n of Examples, Further Structure 3 3 4.1. Th e discrete series of subfactor s 3 3 4.2. Brattel i diagrams of the et algebras 3 6 4.3. Affin e Li e algebra 3 8 4.4. Realizin g the Virasoro discret e series 3 9 4.5. Th e tower of relative commutants 4 0 4.6. Example s of towers of relative commutants 4 2 4.7. Th e relative commutant proble m 4 3 Lecture 5. The Braid Group and Its Representations 4 5 5.1. Definitio n an d presentation 4 5 5.2. Actio n o f the braid grou p on the free group 4 7 5.3. Th e pur e brai d grou p an d th e inductiv e structur e o f th e brai d groups 4 7
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