JournalsprimsVol. 49, No. 1pp. 123–153

Weyl Groups Associated with Affine Reflection Systems of Type A1A_1 (Coxeter Type Defining Relations)

  • Saeid Azam

    University of Isfahan, Iran
  • Mohammad Nikouei

    University of Isfahan, Iran
Weyl Groups Associated with Affine Reflection Systems of Type $A_1$ (Coxeter Type Defining Relations) cover
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Abstract

We off er a presentation for the Weyl group of an affine reflection system RR of type A1A_1 as well as a presentation for the so called hyperbolic Weyl group associated with an affine reflection system of type A1A_1. Applying these presentations to extended affine Weyl groups, and using a description of the center of the hyperbolic Weyl group, we also give a new finite presentation for an extended ane Weyl group of type A1A_1. Our presentation for the (hyperbolic) Weyl group of an affine reflection system of type A1A_1 is the fi rst nontrivial presentation given in this generality, and can be considered as a model for other types.

Cite this article

Saeid Azam, Mohammad Nikouei, Weyl Groups Associated with Affine Reflection Systems of Type A1A_1 (Coxeter Type Defining Relations). Publ. Res. Inst. Math. Sci. 49 (2013), no. 1, pp. 123–153

DOI 10.4171/PRIMS/99