Classification of irreducible representations of Heisenberg groups and algebras
نویسنده
چکیده
Definition. A Heisenberg group for a symplectic vector space (V, ω) is the Lie group with the underlying manifold V ×R and the multiplication (u, s)(v, t) = (u+ v, s+ t+ ω(u, v)/2) where u, v ∈ V and s, t ∈ R. The map t 7→ (0, t) is a Lie group homomorphism from R to the Heisenberg group. Its image coincides with the center of the Heisenberg group. The dimension of the Heisenberg group equals 2n+ 1.
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