scholarly journals Classification of Sylow classes of parabolic and reflection subgroups in unitary reflection groups

2020 ◽  
Vol 48 (9) ◽  
pp. 3989-4001
Author(s):  
Kane Douglas Townsend
Keyword(s):  
Reflection Groups ◽  
Unitary Reflection

scholarly journals Canonical Systems of Basic Invariants for Unitary Reflection Groups

2016 ◽  
Vol 59 (3) ◽  
pp. 617-623 ◽  
Author(s):  
Norihiro Nakashima ◽  
Hiroaki Terao ◽  
Shuhei Tsujie
Keyword(s):  
Explicit Formula ◽  
Reflection Group ◽  
Canonical System ◽  
Reflection Groups ◽  
Canonical Systems ◽  
The Third ◽  
Unitary Reflection ◽  
Unitary Reflection Group

AbstractIt is known that there exists a canonical system for every finite real reflection group. In a previous paper, the first and the third authors obtained an explicit formula for a canonical system. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group.

scholarly journals A Refined Count of Coxeter Element Reflection Factorizations

10.37236/7362 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Elise DelMas ◽  
Thomas Hameister ◽  
Victor Reiner
Keyword(s):  
Generating Function ◽  
Coxeter Element ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Coxeter Number ◽  
Simple Product

For well-generated complex reflection groups, Chapuy and Stump gave a simple product for a generating function counting reflection factorizations of a Coxeter element by their length. This is refined here to record the numberof reflections used from each orbit of hyperplanes. The proof is case-by-case via the classification of well-generated groups. It implies a new expression for the Coxeter number, expressed via data coming from a hyperplane orbit; a case-free proof of this due to J. Michel is included.

Coxeter classes of unitary reflection groups

1995 ◽  
Vol 119 (1) ◽  
pp. 297-316 ◽  
Author(s):  
N. Spaltenstein
Keyword(s):  
Reflection Groups ◽  
Unitary Reflection
Sign in / Sign up

Export Citation Format

Share Document