Annals of Combinatorics

, Volume 9, Issue 4, pp 451–494

Temperley-Lieb Immanants

Original Paper

DOI: 10.1007/s00026-005-0268-0

Cite this article as:
Rhoades, B. & Skandera, M. Ann. Comb. (2005) 9: 451. doi:10.1007/s00026-005-0268-0

Abstract.

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 

Keywords.

Temperley-Lieb algebra immanant total nonnegativity matrix minor 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsXXXHanoverUSA