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arXiv · 2003.03573

Elliptic canonical bases for toric hyper-Kahler manifolds

Tatsuyuki Hikita
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Abstract

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.

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Tatsuyuki Hikita. 2020-03-07. Elliptic canonical bases for toric hyper-Kahler manifolds. https://arxiv.org/abs/2003.03573

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