Modules of the Temperley-Lieb algebra at zero
Abstract
We explicitly describe the category of modules of the Temperley-Lieb algebra TLn(β) under specialization β=0 for even n in terms of a quiver algebra, analogous to a result of Berest-Etingof-Ginzburg. In particular, we explicitly construct an exact sequence of the standard modules of TLn(0), which categorifies a numerical coincidence regarding the evaluation of the Jones polynomial at t=-1. We furthermore deduce a consequence in the representation theory of symmetric groups over characteristic two.
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