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

• Autores: Sarah Reznikoff
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 56, Nº 6, 2007, págs. 3129-3150
• Idioma: inglés
• DOI: 10.1512/iumj.2007.56.3140
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• Resumen

  • 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.