Factorization of Temperley–Lieb diagrams

Dana C. Ernst, Michael G. Hastings, Sarah K. Salmon

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The Temperley–Lieb algebra is a finite-dimensional associative algebra that arose in the context of statistical mechanics and occurs naturally as a quotient of the Hecke algebra arising from a Coxeter group of type A. It is often realized in terms of a certain diagram algebra, where every diagram can be written as a product of “simple diagrams”. These factorizations correspond precisely to factorizations of the so-called fully commutative elements of the Coxeter group that index a particular basis. Given a reduced factorization of a fully commutative element, it is straight-forward to construct the corresponding diagram. On the other hand, it is generally difficult to reconstruct the factorization given an arbitrary diagram. We present an efficient algorithm for obtaining a reduced factorization for a given diagram.

Original languageEnglish (US)
Pages (from-to)89-108
Number of pages20
Issue number1
StatePublished - 2017


  • Coxeter group
  • Temperley–Lieb algebra
  • diagram algebra
  • heap

ASJC Scopus subject areas

  • General Mathematics


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