Stable bases of the Springer resolution and representation theory
Changjian Su, Changlong Zhong
TL;DR
This paper reviews the properties of stable bases in the Springer resolution and explores their connections to Lie algebra representations over various fields and the Langlands dual group, highlighting their significance in geometric representation theory.
Contribution
It consolidates fundamental facts about stable bases and elucidates their relationships with representations of Lie algebras and the Langlands dual group across different mathematical settings.
Findings
Clarifies the role of stable bases in Springer resolution
Links stable bases to Lie algebra representations over complex and positive characteristic fields
Connects stable bases to the Langlands dual group in non-Archimedean contexts
Abstract
In this note, we collect basic facts about Maulik and Okounkov's stable bases for the Springer resolution, focusing on their relations to representations of Lie algebras over complex numbers and algebraically closed positive characteristic fields, and of the Langlands dual group over non-Archimedean local fields.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra