Graduate Student Seminar-Fully Commutative Elements in Complex Reflection Groups

Date and Time: Friday, October 29th, 2-3pm

Place: Rome 206

Speaker: Jiayuan Wang GWU

Title: Fully Commutative Elements in Complex Reflection Groups

Abstract: An element is fully commutative if any two of its reduced expressions are related by a series of interchanges of adjacent commuting generators. Fully commutative elements in Coxeter groups $B_n$ and $D_n$ are completely characterized and counted by Stembridge. Feinberg-Kim-Lee-Oh have extended the study of fully commutative elements from Coxeter groups to the complex setting, giving an enumeration of such elements in complex reflection groups $G(m,1,n)$. In this talk, we will present a combinatorial connection between fully commutative elements in $B_n$ and $G(m,1,n)$, which allows us to characterize fully commutative elements in $G(m,1,n)$ by pattern avoidance and enumerate them. Further, we will show that fully commutative elements in $G(m,m,n)$ do not have the pattern avoidance property and we will explore full commutativity in $G(m,m,n)$ with different generating sets.