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Temperley-Lieb Immanants
Brendon Rhoades and Mark Skandera
Department of Mathematics 6188 Bradley Hall Dartmouth College, Hanover, NH 03755-3551, USA
brhoades@umich.edu, Mark.Skandera@dartmouth.edu
Annals of Combinatorics 9 (4) p.451-494 December, 2005
AMS Subject Classification: 15A15, 05E15, 20C08
Abstract:
We use the Temperley-Lieb algebra to define a family of totally nonnegative polynomials of the form . The cone generated by these polynomials contains all totally nonnegative polynomials of the form , where are matrix minors. We also give new conditions on the sets I,…,K', which characterize differences of products of minors which are totally nonnegative.
Keywords: Temperley-Lieb algebra, immanant, total nonnegativity, matrix minor

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