2015/09/03 by Harbat, Sadek Al
#20F36 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1509.01033
We define a tower of injections of C-type Coxeter groups W( Cn) for n≥ 1. We define a tower of Hecke algebras and we use the faithfulness at the Coxeter level to show that this last tower is a tower of injections. Let Wc( Cn) be the set of fully commutative elements in W( Cn), we classify the elements of Wc( Cn) and give a normal form for them. We use this normal form to define two injections from Wc( Cn-1) into Wc( Cn). We then define the tower of affine Temperley-Lieb algebras of type C and use the injections above to prove the faithfulness of this tower.