Work

A Geometric Realization of the Centre of the Small Quantum Group

Year: 2026

Type: article

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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748026102011

Authors: Roman Bezrukavnikov, Pablo Boixeda Alvarez, Peng Shan, Eric Vasserot

Institutions: Massachusetts Institute of Technology, Yale University, Tsinghua University, Université Paris Cité

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Research in Mathematics