On Involutions of Minuscule Kirillov Algebras Induced by Real Structures
Abstract
Abstract We study Kirillov algebras attached to minuscule highest weight representations of semisimple Lie algebras. They can be viewed as equivariant cohomology algebras of partial flag varieties. Real structures on the varieties then induce involutions of these algebras. We describe how these involutions act on the spectra of minuscule Kirillov algebras, and model the fixed points via the equivariant cohomology of real partial flag varieties. We then use this model to characterise freeness of the fixed point coordinate ring over the appropriate base. As an application, we recover a $$q=-1$$ phenomenon of Stembridge in the minuscule case by geometric means.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Algebra and Logic
Matrix Theory and Algorithms
Publication details
- Journal / source
- Transformation Groups
- Publisher
- Springer Science and Business Media LLC
- Volume
- 31
- Issue
- 3
- Pages
- 2709–2749
- Publication date
- 14 March 2026
- Language
- EN