Intertwining operators and geometry

Exceptional complex dual pair correspondences

24 janv. 2025, 10:30

50m

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Hung Yean Loke (National University of Singapore)

Description

Let ${\mathrm{E}}_n(\mathbb{C})$ denote the connected complex Lie group of type ${\mathrm{E}}_n$ for $n=6,7$. These two groups contain the following reductive pairs:
$$\begin{array}{rl}{T}_1(\mathbb{C})\times \mathrm{Spin}(10,\mathbb{C})& \subset {\mathrm{E}}_6(\mathbb{C}),\\ T_2(\mathbb{C})\times \mathrm{Spin}(8,\mathbb{C})& \subset {\mathrm{E}}_6(\mathbb{C}),\\ T_1(\mathbb{C})\times {\mathrm{E}}_6(\mathbb{C})& \subset {\mathrm{E}}_7(\mathbb{C}),\end{array}$$ where $T_1(\mathbb{C})$ and $T_2(\mathbb{C})$ are complex tori of dimensions 1 and 2 respectively. In this talk, I will describe the dual pair correspondences arising from the minimal representations of ${\mathrm{E}}_6(\mathbb{C})$ and ${\mathrm{E}}_7(\mathbb{C})$. These are joint projects with Edmund Karasiewicz and Gordan Savin.