  An operator fractional Brownian field (OFBF) is a Gaussian, stationary
increment R^n-valued random field on R^m that satisfies the operator
self-similarity property {X(c^E t)}_{t in R^m} L= {c^H X(t)}_{t in R^m}, c > 0,
for two matrix exponents (E,H). In this paper, we characterize the domain and
range symmetries of OFBF, respectively, as maximal groups with respect to
equivalence classes generated by orbits and, based on a new anisotropic
polar-harmonizable representation of OFBF, as intersections of centralizers. We
also describe the sets of possible pairs of domain and range symmetry groups in
dimensions (m,1) and (2,2).
