Cyclotomic root systems and bad primes

2017/04/12 by Broué, Michel, Corran, Ruth, Michel, Jean
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1704.03779

Abstract

We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root systems over the field of definition k of the reflection representation. In the case of spetsial reflection groups, we generalize as well the definition and properties of bad primes.

Related

• Root systems in number fields
• On Rank 2 Complex Reflection Groups
• Classification of the root systems R(m)
• Root Graded Groups
• Projective reflection groups