The Gram Matrix of a Temperley-lieb Algebra Is Similar to the Matrix of Chromatic Joins
نویسندگان
چکیده
Rodica Simion noticed experimentally that matrices of chromatic joins (introduced by W. Tutte in [Tu2]) and the Gram matrix of the Temperley-Lieb algebra, have the same determinant, up to renormalization. In the type A case, she was able to prove this by comparing the known formulas: by Tutte and R. Dahab [Tu2, Dah], in the case of chromatic joins, and by P. Di Francesco, and B. Westbury [DiF, We] (based on the work by K. H. Ko and L. Smolinsky [KS]) in the Temperley-Lieb case; see [CSS]. She then asked for a direct proof of this fact [CSS], [Sch], Problem 7.
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