Temperley-Lieb planar algebra modules arising from the ADE planar algebras |
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Authors: | Sarah A. Reznikoff |
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Affiliation: | Department of Mathematics, Smith College Northampton, MA 01063, USA |
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Abstract: | A Hilbert module over a planar algebra P is essentially a Hilbert module over a canonically defined algebra spanned by the annular tangles in P. It follows that any planar algebra Q containing P is a module over P, and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar algebra with the same modulus. We describe a positivity result that allows us to describe irreducible Temperley-Lieb planar algebra modules, and apply the result to decompose the planar algebras determined by the Coxeter graphs An (n?3), Dn (n?4), E6, E7, and E8. |
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Keywords: | Subfactors and their classification |
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