Reflexponents

2019/02/17 by Nathan Williams, Williams, Nathan
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1902.06264

openalex publication_date 2019/02/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes using similar invariants we call reflexponents. Our verifications are case-by-case.

Related

• Fundamental theorems for invariants of a class of pseudo-reflection groups
• Invariant differential derivations for reflection groups in positive characteristic
• Reflection groups acting on their hyperplanes
• Basic Invariants of the Complex Reflection Group No.34 Constructed by Conway and Sloane
• Normal Reflection Subgroups