Dimension bound from paired Clifford involutions
= Dimension bound from paired Clifford involutions
{title2=$\dim V\geq2^n$}
For $2n$ hermitian Euclidean Clifford generators, the commuting hermitian involutions $J_j=i\gamma^{2j-1}\gamma^{2j}$ admit a common eigenvector. Each odd-indexed generator flips one joint eigenvalue. The $2^n$ resulting vectors are nonzero and mutually orthogonal. Thus any nonzero invariant complex representation has dimension at least $2^n$.