# Darstellungstheorietage and Nikolaus Conference 2021

Speaker: Laura Voggesberger (Kaiserslautern)

Title: An Introduction to Nilpotent Pieces

Abstract:

Let $$G$$ be a connected reductive algebraic group over an algebraically closed field $$k$$, and let Lie$$(G)$$ be its associated Lie algebra. In 2011, Lusztig defined a partition of the unipotent variety of $$G$$. This partition is very useful when working with representations of $$G$$. Equivalently, one can consider certain subsets of the nilpotent variety of $$g$$ called pieces. This approach appears in Lusztig’s article. The pieces for the exceptional groups of type $$G_2$$, $$F_4$$, $$E_6$$, $$E_7$$ and $$E_8$$ in bad characteristic have not yet been determined. In this talk, I will give an introduction to both definitions of the nilpotent pieces and present a solution to this problem for groups of type $$G_2$$ and $$F_4$$.