Annals of Combinatorics

, Volume 9, Issue 4, pp 451–494

Temperley-Lieb Immanants

Authors

    • Department of MathematicsXXX
  • Mark Skandera
    • Department of MathematicsXXX
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.

15A1505E1520C08

Keywords.

Temperley-Lieb algebraimmananttotal nonnegativitymatrix minor

Copyright information

© Birkhäuser Verlag, Basel 2005