Zariski theorems and diagrams for braid groups

By David Bessis. 2000

62 citations recorded by the source corpus.

Abstract.Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d1c99dfd9432d1122df39a196ba10b8685046fd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. W. Couwenberg
2. G. Heckman
3. E. Looijenga
4. David Bessis
5. Nathan Reading
6. Drew Armstrong
7. Michelle L. Wachs
8. Jon McCammond

In Geometry and Topology

1. E. Looijenga
2. David Bessis
3. W. Couwenberg
4. G. Heckman
5. Igor Dolgachev
6. Nathan Reading
7. Drew Armstrong
8. Alexander Perry

In Mathematical Physics

1. E. Looijenga
2. David Bessis
3. W. Couwenberg
4. G. Heckman
5. Igor Dolgachev
6. Alexander Perry
7. R. Laza
8. Emanuele Macrì

Citations in the corpus

• The representation theory of the Ariki-Koike and cyclotomic q-Schur algebras (2002, unknown): “Finally, let WλO and W λ R be the Weyl modules for SO(Λ) and SR(Λ) respectively; note that WλR ∼= WλO ⊗O R as R-modules.”
• Geometric Structures on the Complement of a Projective Arrangement (2003, methodology): “For the case of an arbitrary finite complex reflection group, one may use a presentation of the fundamental group due to Bessis [2].”
• Finite complex reection arrangements are K(; 1) (2015, background): “If P is Xn-monic, the fibration p : E → Y −K is split.”
• Finite complex reflection arrangements are $K(\pi,1)$ (2006, unknown): “(v) ⇒ (i) follows from the main result in [2].”