2020/03/07 by Tatsuyuki Hikita, Hikita, Tatsuyuki · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2003.03573
openalex publication_date 2020/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lusztig defined certain involutions on the equivariant K-theory of Slodowy varieties and gave a characterization of certain bases called canonical bases. In this paper, we give a conjectural generalization of these involutions and K-theoretic canonical bases to conical symplectic resolutions which have good Hamiltonian torus actions and state several conjectures related to them which we check for toric hyper-Kahler manifolds. We also propose an elliptic analogue of these bar involutions. As a verification of our proposal, we explicitly construct elliptic lifts of K-theoretic canonical bases and prove that they are invariant under elliptic bar involutions for toric hyper-Kahler manifolds.