A finite presentation for extended affine Weyl groups (simply laced types)

Saeid Azam; Valiollah Shahsanaei

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A finite presentation for extended affine Weyl groups (simply laced types)

Saeid Azam·Valiollah Shahsanaei

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Abstract

Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities $\leq 2$, where for nullity 2 there is only one known such presentation. We give a finite presentation for the class of simply laced extended affine Weyl groups. Our presentation is nullity free if rank $>1$ and for rank 1 it is given for nullities $\leq 3$. The generators and relations are given uniformly for all types, and for a given nullity they can be read from the corresponding finite Cartan matrix and the semilattice involved in the structure of the root system.

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BibTeX RIS

Saeid Azam, Valiollah Shahsanaei. 2006-07-11. A finite presentation for extended affine Weyl groups (simply laced types). https://arxiv.org/abs/math/0604401

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