2022/03/16 by Biagioli, Riccardo, Calussi, Gabriele, Fatabbi, Giuliana
#05E10 #16G30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2203.08530
In this paper we propose a combinatorial framework to study a diagrammatic representation of the affine Temperley-Lieb algebra of type C introduced by Ernst. In doing this, we define two procedures, a decoration algorithm on diagrams and a reduction algorithm on heaps of independent interest. Using this approach, an explicit algorithmic description of Ernst representation map is provided from which its faithfulness can be deduced. We also give a construction of the inverse map.