  The corner symmetry algebra organises the physical charges induced by gravity
on codimension-$2$ corners of a manifold. In this letter, we initiate a study
of the quantum properties of this group. We first describe the central
extensions and how the quantum corner symmetry group arises. We then classify
the Casimirs and the induced unitary irreducible representation. We finally
discuss the gluing of corners, achieved identifying the maximal commuting
sub-algebra. This is a concrete implementation of the gravitational constraints
at the quantum level, via the entangling product.
