Hurwitz Actions on Reflection Factorizations in Complex Reflection Group G₆

Authors

Gaurav Gawankar, George Washington UniversityFollow
Dounia Lazreq, George Washington UniversityFollow
Mehr Rai, George Washington UniversityFollow
Seth Sabar, School Without WallsFollow

Abstract

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.

Faculty Sponsor

Joel Lewis

Recommended Citation

Gawankar, Gaurav; Lazreq, Dounia; Rai, Mehr; and Sabar, Seth (2021) "Hurwitz Actions on Reflection Factorizations in Complex Reflection Group G₆," Rose-Hulman Undergraduate Mathematics Journal: Vol. 22: Iss. 2, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss2/6