University of Minnesota Combinatorics Seminar: 2020-2021

Date: 10/09/2020

Speaker: Sarah Brauner

Eulerian Representations for Coincidental Reflection Groups
The Eulerian idempotents of a real reflection group and the representations they generate are a topic of longstanding interest to combinatorialists, representation theorists and topologists. In Type A, these representations have connections to the braid arrangement, Solomon's descent algebra, and mysteriously arise as the graded pieces of the cohomology of the configuration space of $n$ ordered points in $\mathbb{R}^3$. In this talk, I will describe how this relationship generalizes to real reflection groups of coincidental type---that is, reflection groups whose exponents form an arithmetic progression---by characterizing the Eulerian representations as (among other things) components of the associated graded Varchenko-Gelfand ring. All of the above concepts will be defined during the talk.

Eulerian Representations for Coincidental Reflection Groups

The Eulerian idempotents of a real reflection group and the representations they generate are a topic of longstanding interest to combinatorialists, representation theorists and topologists. In Type A, these representations have connections to the braid arrangement, Solomon's descent algebra, and mysteriously arise as the graded pieces of the cohomology of the configuration space of $n$ ordered points in $\mathbb{R}^3$. In this talk, I will describe how this relationship generalizes to real reflection groups of coincidental type---that is, reflection groups whose exponents form an arithmetic progression---by characterizing the Eulerian representations as (among other things) components of the associated graded Varchenko-Gelfand ring. All of the above concepts will be defined during the talk.