Séminaire Lotharingien de Combinatoire, 85B.19 (2021), 12 pp.

Joel Brewster Lewis and Jiayuan Wang

The Hurwitz Action in Complex Rreflection Groups

Abstract. We study the reflection factorizations of an arbitrary element in the complex reflection groups G(m,p,n) under the Hurwitz action. Using combinatorial and graph theoretical techniques, we present an if-and-only-if statement of when two factorizations are Hurwitz equivalent. Then we prove a formula that counts the number of Hurwitz orbits of an arbitrary element.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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