Quantizations of multiplicative hypertoric varieties at a root of unity

Abstract

We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework.

arXiv comment26 pages

References in corpus (10)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• Quantizations of conical symplectic resolutions I: local and global structure
• Toric Hyperkahler Varieties
• Hypertoric category O
• Global Weyl groups and a new theory of multiplicative quiver varieties
• Morita theory in abelian, derived and stable model categories
• Quantized multiplicative quiver varieties
• Quantum Cohomology of Hypertoric Varieties
• Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties
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Cited by in corpus (6)

• The Harish-Chandra isomorphism for quantum GL_2
• Quantum Weyl algebras and reflection equation algebras at a root of unity
• Quantum Multiplicative Hypertoric Varieties and Localization
• Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
• Homological Mirror Symmetry for Hypertoric Varieties I
• SYZ mirror symmetry for hypertoric varieties