Generically constrained quantum isotropy

Let V be a finite-dimensional unitary representation of a compact quantum group G and denote by GW the isotropy subgroup of a linear subspace W≤ V regarded as a point in the Grassmannian G(V) . We show that the space of those W∈ G(V) for which GW acts trivially on W (or V ) is open in the Zariski topology of the Weil restriction ResC/RG(V) . More generally, this holds for the space of W for which (a) the GW -action factors through its abelianization or (b) the summands of the GW -representation on W (or V ) are otherwise dimensionally constrained. The results generalize analogous classical generic rigidity statements useful in establishing the triviality of the classical automorphism groups of random quantum graphs in the matrix algebra Mₙ and can be put to similar use in fully non-commutative versions of those results (quantum graphs, quantum groups).