%0 Journal Article
%T The Center of the Nilcoxeter and 0-Hecke Algebras
%A Joelle Brichard
%J Mathematics
%D 2008
%I arXiv
%X We compute the dimension of the center of the 0-Hecke algebra $\mathcal{H}_n$ and of the Nilcoxeter algebra $\mathcal{NC}_n$ using a calculus of diagrams on the M\"{o}bius band. In the case of the Nilcoxeter algebra, this calculus is shown to produce a basis for $Z(\mathcal{NC}_n)$ and the table of multiplication in this basis is shown to be trivial. We conjecture that a basis for $Z(\mathcal{H}_n)$ can also be obtained in a specific way from this topological calculus.
%U http://arxiv.org/abs/0811.2590v1