Group representation

Symplectic representation

A symplectic representation 𝔛 of 𝐺 is a group homomorphism 𝔛 :𝐺 →Sp⁡(𝑉) into the symplectic group #m/def/rep2 where 𝑉 is a symplectic vector space. Thus 𝔛 is a group representation of 𝐺 carried by 𝑉 such that

for all 𝑔 ∈𝐺 and 𝑣,𝑤 ∈𝑉 where 𝜔 is the symplectic form.

Properties

• A group representation is self-dual iff it preserves a nondegenerate bilinear form

#state/tidy | #lang/en | #SemBr