Cyclic sieving for generalised non-crossing partitions associated to complex reflection groups of exceptional type

TL;DR

This paper proves cyclic sieving conjectures for generalized non-crossing partitions linked to 26 exceptional well-generated complex reflection groups, confirming their combinatorial symmetry properties.

Contribution

It provides the first complete proof of the cyclic sieving conjectures for all exceptional complex reflection groups, extending previous results to a broader class.

Findings

Confirmed cyclic sieving conjectures for 26 exceptional groups

Established combinatorial symmetry properties of non-crossing partitions

Provided detailed computational proofs in supplementary material

Abstract

We present the proof of the cyclic sieving conjectures for generalised non-crossing partitions associated to well-generated complex reflection groups due to Armstrong, respectively to Bessis and Reiner, for the 26 exceptional well-generated complex reflection groups. The computational details are provided in the manuscript "Cyclic sieving for generalised non-crossing partitions associated to complex reflection groups of exceptional type - the details" [arXiv:1001.0030].