The connection between representation theory and Schubert calculus
Harry Tamvakis
TL;DR
This paper explores the link between the representation theory of the general linear group and Schubert calculus on the Grassmannian, using Chern-Weil theory, and discusses why similar approaches differ for other Lie groups.
Contribution
It establishes a direct connection between representation theory and Schubert calculus via characteristic classes, highlighting differences for other Lie groups.
Findings
Connection established between representation theory and Schubert calculus
Uses Chern-Weil theory to explain the link
Shows why similar methods differ for other Lie groups
Abstract
We describe a direct connection between the representation theory of the general linear group and classical Schubert calculus on the Grassmannian, which goes via the Chern-Weil theory of characteristic classes. We also explain why the analogous constructions do not give the same result for other Lie groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models