Group representation Symplectic representation A symplectic representation π of πΊ is a group homomorphism π :πΊ βSpβ‘(π) into the symplectic group rep2 where π is a symplectic vector space. Thus π is a group representation of πΊ carried by π such that π(π(π)π£,π(π)π€)=0 for all π βπΊ and π£,π€ βπ where π is the symplectic form. Properties A group representation is self-dual iff it preserves a nondegenerate bilinear form tidy | en | SemBr