# Darstellungstheorietage and Nikolaus Conference 2021

Speaker: Nathan Chapelier (Tours)

Title: Shi Variety Corresponding to an Affine Weyl Group

Abstract:

For each irreducible affine Weyl group $$W_a$$ we will see that there exists a bijection between $$W_a$$ and the integral points of an affine variety, denoted $$X_{W_a}$$ and called the Shi variety of $$W_a$$. Subsequently, we will give some combinatorial and geometric properties of this variety. We will lay stress on type $$A$$ to illustrate these properties.