  We definitively solve the old problem of finding a minimal integrity basis of
polynomial invariants of the fourth-order elasticity tensor C. Decomposing C
into its SO(3)-irreducible components we reduce this problem to finding joint
invariants of a triplet (a, b, D), where a and b are second-order harmonic
tensors, and D is a fourth-order harmonic tensor. Combining theorems of
classical invariant theory and formal computations, a minimal integrity basis
of 297 polynomial invariants for the elasticity tensor is obtained for the
first time.
