In this paper, we prove that a simple system for a subsystem Ψ of the complex root system Φ can always be chosen as a subset of the positive system Φ+of Φ.

It is proved that a simple system for a subsystem Ψ of the complex root system Φ can always be chosen as a subset of the positive systemΦ+ of Φ. In this ...

We describe a class of groups with the property that the finite ones among them are precisely the complex reflection groups of rank two.

Nov 1, 1998 · Simulating a complex luminaire such as a chandelier is expensive and slow, even using state-of-the-art algorithms.

We show that Molchanov's speculation is false in general but holds for all coincidental complex reflection groups when appropriately modified using exponents ...

Apr 28, 2024 · Complex reflection groups of rank two are precisely the finite groups in the family of groups that we call virtual complex reflection groups of ...

Some general results are also obtained by studying the action of a Coxeter group on the Stanley-Reisner ring of the corresponding Coxeter complex. In the ...

Our aim is to carry out analogous calculations for complex reflection groups, in the hope that the results describe some as-yet unknown “unipotent variety” in ...

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics ...

Sep 5, 2019 · One of many results in this area is a formula of Jackson for the generating function that counts factorizations of an n-cycle as a product ...