Instantons on ALE spaces for classical groups, involutions on quiver varieties, and quantum symmetric pairs

2025/10/14 by Hiraku Nakajima, Nakajima, Hiraku · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2510.13007

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

Moduli spaces of instantons on ALE spaces for classical groups are examples of fixed point sets of involutions on quiver varieties, i.e., σ-quiver varieties. In 2018 Yiqiang Li considered their equivariant cohomology, and by stable envelope of Maulik-Okounkov, constructed representations of coideal subalgebras of Maulik-Okounkov Yangian, called twisted Yangian. We calculate K-matrices as matrices in examples, identified the twisted Yangians with ones studied in other literature, and clarify conditions which we should impose to make them well-defined.

Cited by

• Freidel-Maillet type equations on fused K-matrices over the positive part of U_q(\widehat\mathfraksl₂)
• Minimalistic Presentation and Coideal Structure of Twisted Yangians

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