Original Paper

Annals of Combinatorics

, Volume 9, Issue 4, pp 451-494

First online:

Temperley-Lieb Immanants

  • Brendon RhoadesAffiliated withDepartment of Mathematics, XXX Email author 
  • , Mark SkanderaAffiliated withDepartment of Mathematics, XXX

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We use the Temperley-Lieb algebra to define a family of totally nonnegative polynomials of the form \( \Sigma _{{\upsigma \in S_{n} }} f(\upsigma )x_{{1,\upsigma (1)}} \cdots x_{{n,\upsigma (n)}} \). The cone generated by these polynomials contains all totally nonnegative polynomials of the form \( \Delta _{{J,J' }} (x)\Delta _{{L,L' }} (x) - \Delta _{{I,I' }} (x)\Delta _{{K,K' }} (x) \), where, \( \Delta _{{I,I' }} (x), \ldots ,\Delta _{{K,K' }} (x) \) are matrix minors. We also give new conditions on the sets I,...,K′ which characterize differences of products of minors which are totally nonnegative.

AMS Subject Classification.

15A15 05E15 20C08


Temperley-Lieb algebra immanant total nonnegativity matrix minor