Maffei's action and symplectic Springer action for quiver varieties

2024/03/28 by Yaochen Wu, Wu, Yaochen
Mathematics · #16G20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2403.19823

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the relationship between the actions of two Weyl groups on the cohomology of a smooth quiver variety: the Maffei's action of the Weyl group associated to the quiver, and the symplectic Springer action of the Namikawa-Weyl group of the affine quiver variety. We show there is a natural map from the former group to the latter, which is an embedding in favorable situations, and this map intertwines their actions on the cohomology. This answers a question raised in arXiv:1904.10497.

Related

• Springer theory for symplectic Galois groups
• Homological realization of Nakajima varieties and Weyl group actions
• Quivers, Invariants and Quotient Correspondence
• A remark on quiver varieties andweyl groups
• Namikawa-Weyl groups of affinizations of smooth Nakajima quiver varieties