Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Yu Li
Affiliation:

MPIM
Date:

Thu, 17/02/2022 - 15:00 - 16:00 Let $H$ be a Cartan subgroup of a semisimple algebraic group $G$ over the complex numbers. The wonderful compactification $\bar H$ of $H$ was introduced and studied by De Concini and Procesi. For the Lie algebra $\mathfrak h$ of $H$, we define an analogous compactification $\bar {\mathfrak h}$ of $\mathfrak h$, to be referred to as the wonderful compactification of $\mathfrak h$, as a subvariety of a variety of Lagrangian subalgebras. We will describe various properties of the cohomology of $\bar {\mathfrak h}$. In particular, we will connect the Betti numbers of $\bar {\mathfrak h}$ with some classical combinatorial sequences (Stirling numbers, Whitney numbers of the Dowling lattice, etc.). The ring structure of the cohomology of $\bar {\mathfrak h}$ will be explained in terms of the intersection lattice of the Coxeter hyperplane arrangement.

This is joint work with Sam Evens.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158