The Center of the Nilcoxeter and 0-Hecke Algebras

Abstract

We compute the dimension of the center of the 0-Hecke algebra ${\mathcal{H}}_n$ and of the Nilcoxeter algebra ${\mathcal{N}\mathcal{C}}_n$ using a calculus of diagrams on the Möbius band. In the case of the Nilcoxeter algebra, this calculus is shown to produce a basis for $Z({\mathcal{N}\mathcal{C}}_n)$ 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.

28 pages, 25 figures