Resumen de Coefficients of the one- and two-gap boxes in the Jones-Wenzl idempotent

Sarah Reznikoff

• The first n - 1 projections forming the Jones tower of a II1 subfactor generate a semisimple quotient,TLn.., of the Temperley- Lieb Algebra. This algebra can be represented pictorially by planar diagrams on n strings in a box, and these diagrams can be classified according to the number of non-through strings, or �gaps� they have. The Jones-Wenzl Idempotent is the complement in TLn.. of the supremum of the projections generating the Jones tower. We prove Ocneanu�s formula for the coefficients of the one- and two-gap boxes in an explicit expression of this element.