کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4584517 | 1630487 | 2015 | 39 صفحه PDF | دانلود رایگان |
We obtain new presentations for the imprimitive complex reflection groups of type (de,e,r)(de,e,r) and their braid groups B(de,e,r)B(de,e,r) for d,r≥2d,r≥2. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group B(de,e,r)B(de,e,r) is a semidirect product of the braid group of affine type A˜r−1 and an infinite cyclic group. Elements of B(de,e,r)B(de,e,r) are visualised as geometric braids on r+1r+1 strings whose first string is pure and whose winding number is a multiple of e . We classify periodic elements, and show that the roots are unique up to conjugacy and that the braid group B(de,e,r)B(de,e,r) is strongly translation discrete.
Journal: Journal of Algebra - Volume 427, 1 April 2015, Pages 387–425