In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the order ... Definitions · Coxeter elements · Coxeter plane

Coxeter elements form a distinguished conjugacy class in each finite Euclidean reflection group. This chapter concerns their order. We shall show that, ...

In mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating ...

Furthermore, we obtain some direct formulae of c(W) for a large family of Coxeter groups, which include all the finite, affine and hyperbolic Coxeter groups.

15 авг. 2018 г. · The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and ...

A Coxeter element of W is by definition a product of all generators s S in any fixed order. We use the notation C(W) to denote the set of all the Coxeter ...

24 сент. 2017 г. · A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, ...

These elements play an important role in the theory of Coxeter groups, e.g., the determination of polynomial invariants, the Poincar polynomial, the Coxeter ...

— Let g be a complex simple Lie algebra and let h = h(g) be its Coxeter number. By definition h is the order of the Coxeter element in a Weyl group of g. If / = ...

30 нояб. 2021 г. · For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This ...