Poincaré series of the spaces of commuting elements

2021/01/25 Mon 17:00 - 18:00
Masahiro Takeda
Kyoto University

Let $G$ be a compact connected Lie group, and let Hom$(\mathbb{Z}^m,G)$ denote the space of commuting $m$-tuples in $G$. Baird proved that the cohomology of Hom$(\mathbb{Z}^m,G)$ is identified with a certain ring of invariants of the Weyl group of $G$. Therefore the cohomology of Hom$(\mathbb{Z}^m,G)$ is important not only in topology but also in representation theory. We will talk about the Poincaré series of the cohomology of Hom$(\mathbb{Z}^m,G)$ for classical groups $G$ and some applications. This talk is based on joint work with Daisuke Kishimoto.

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