  We propose to use interpolation categories to study PBW deformations, and
demonstrate this idea for the orthosymplectic supergroups. Employing a
combinatorial calculus based on pseudographs and partitions which we derive
from a suitable Jacobi identity, we classify PBW deformations in (quotients of)
Deligne's interpolation categories for the orthosymplectic groups. As special
cases, our classification recovers families of infinitesimal Hecke algebras
found by Etingof-Gan-Ginzburg (2005) for the symplectic groups and by
Tsymbaliuk (2015) for the orthogonal groups together with their respective
standard representations using completely different geometric methods. Our
results can be viewed as an extension of these known results to the family of
all orthosymplectic groups together with all of their fundamental
representations, obtained by novel interpolation techniques for PBW
deformations.
