Jonathan Elmer

Description

Title: Modular co/invariants

Abstract:
Let $G$ be a group and $V$, $W$ finite $\mathbb{F}G$-modules. Classically speaking, a covariant is a $G$-equivariant polynomial function $V \to W$. The set of covariants $\mathbb{F}[V,W]^G$ forms a module over the set of invariants $\mathbb{F}[V]^G$. Rather less is known about the structure of $\mathbb{F}[V,W]^G$ as a $\mathbb{F}[V]^G$-module in the modular case ($\operatorname{char} \mathbb{F}$ divides $|G|$) than in the non-modular case. I'll give an overview of what we know, talk about recent work constructing generating sets for $\mathbb{F}[V,W]^G$ when $G$ is cyclic, and describe an unexpected connection with modular coinvariants. In part this is joint work with Mufit Sezer (Bilkent).

Period	18 Feb 2019
Visiting from	Middlesex University (United Kingdom)
Visitor degree	PhD
Degree of Recognition	Local