A Lie-theoretic generalization of some Hilbert schemes

Abstract: I will introduce several varieties attached to a complex reductive group, generalizing for example $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Haiman’s isospectral Hilbert scheme, which pertain to the $\mathsf{GL}_n$-case. I will then explain what is currently known about these varieties (including some low-rank examples) and what else one would like to know about them.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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