Existence and uniqueness of deformation and quantization

Establish the existence and uniqueness, for Hamiltonian \(G\)-actions with moment maps, of the deformation to quasi-Hamiltonian actions and the subsequent shifted geometric quantization to braided module categories over \(\operatorname{Rep}_q(G)\).

Background

The paper identifies a conceptual chain from Hamiltonian actions to quasi-Hamiltonian actions and then to braided module categories, which would connect relative Langlands boundary conditions to skein-theoretic defects. Beyond the quantum symmetric-pair examples treated in the paper, the existence and uniqueness of both stages are not established.

References

At our current level of understanding, both the existence and the uniqueness of the deformation'' andquantization'' arrows are unclear.

— Skein theory, line defects, and quantum symmetric pairs  (2609.18902 - Chen et al., 16 Sep 2026) in Section 1, subsection “Deformation, quantization, and shifted symplectic geometry”