The symmetry properties of "β": "S" ⊗ "S" → C can be determined using Clifford algebras or representation theory. In fact much more can be said: the tensor square "S" ⊗ "S" must decompose into a direct sum of "k"-forms on "V" for various "k", because its weights are all elements in h∗ whose components belong to {−1,0,1}. Now equivariant linear maps "S" ⊗ "S" → ∧"k""V"∗ correspond bijectively to invariant maps ∧"k""V" ⊗ "S" ⊗ "S" → C and nonzero such maps can be constructed via the inclusion of ∧"k""V" into the Clifford algebra. Furthermore, if "β"("φ","ψ") = "ε" "β"("ψ","φ") and "τ" has sign "ε""k" on ∧"k""V" then