Scholarlink

<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q=-1\)</EquationSource> </InlineEquation> phenomenon of Stembridge in the minuscule case by geometric means.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Involutions of Minuscule Kirillov Algebras Induced by Real Structures

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月14日

查看全文
  • Mischa Elkner

摘要

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.