We show that in the complex reflection group G6, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.

Author Bio

Gaurav Gawankar is a recent graduate of the George Washington University, where he studied mathematics and international affairs. He is currently working as a data analyst and plans to start his Ph.D. in mathematics soon.

Dounia Lazreq is a first-year graduate student of mathematics at the University of Virginia. She plans to pursue study in algebraic combinatorics. Outside of research, she is interested in teaching, particularly in proof-based courses for students of different mathematical backgrounds and aspirations.

Mehr Rai graduated in the spring of 2021 from the George Washington University with a bachelor of science in pure mathematics and a minor in physics. She intends on getting a Ph.D. in mathematics in pursuit of a career in teaching and research.

Seth Sabar is a sophomore at Brown University pursuing a Bachelor of Science in math and a Bachelor of Arts in computer science. He's not sure what he wants to do after college yet, but he's excited to keep learning.