Journal of the Institute of Mathematics of Jussieu· 2026Q1
A GEOMETRIC REALIZATION OF THE CENTRE OF THE SMALL QUANTUM GROUP
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- Q1SCImago
- 2026year
Short summary
A new geometric model for the centre of the small quantum group is proposed, using the cohomology of affine Springer fibres.
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Key points
- A geometric model for the centre of the small quantum group is constructed using affine Springer fibres.
- An isomorphism is established between the equivariant cohomology of affine Spaltenstein fibres and the centre of deformed graded modules for the small quantum group.
- An embedding from non-equivariant cohomology invariants to the G-invariant centre is conjectured to be an isomorphism.
- A dimension formula for cohomology invariants provides a lower bound for the dimension of the centre.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We propose a new geometric model for the centre of the small quantum group using the cohomology of certain affine Springer fibres. More precisely, we establish an isomorphism between the equivariant cohomology of affine Spaltenstein fibres for a split element and the centre of the deformed graded modules for the small quantum group. We also obtain an embedding from the invariant part of the non-equivariant cohomology under the action of the extended affine Weyl group to the G ˇ ${\check G}$ ModifyingAbove upper G With ˇ -invariant part of the centre of the small quantum group, which we conjecture to be an isomorphism. Finally, we give a dimension formula for the invariants on the cohomology side, thus providing a lower bound for the dimension of the centre.
The authors' abstract, as published at the source. Journal of the Institute of Mathematics of Jussieu, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics