An introduction to affine Grassmannians and the geometric Satake equivalence
Xinwen Zhu
TL;DR
This paper introduces affine Grassmannians, explores their geometric properties, and discusses the geometric Satake equivalence, providing comprehensive lecture notes for a summer school mini-course.
Contribution
It offers an expanded, detailed introduction to affine Grassmannians and the geometric Satake equivalence, with updated references and additional insights.
Findings
Detailed descriptions of affine Grassmannians
Applications of geometric properties discussed
Clarification of the geometric Satake equivalence
Abstract
We introduce various affine Grassmannians, study their geometric properties, and give some applications. We also discuss the geometric Satake equivalence. These are the expanded lecture notes for a mini-course in 2015 PCMI summer school. References updated and more details added.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry