The Center of the Nilcoxeter and 0-Hecke Algebras

Details The Center of the Nilcoxeter and 0-Hecke Algebras The Center of the Nilcoxeter and 0-Hecke Algebras

2008-11-16

arxiv.org/abs/0811.2590v1

Mathematics

Rings and Algebras

28 pages, 25 figures

Scientific paper

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.

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