Cohomology of the Heisenberg Manifold Sequence

We describe the cohomological structure of the sequence of Heisenberg nilmanifolds \({M}_{H}^{2n-1}\to {M}_{H}^{2n+1}\) $M_H^{2n-1}\to M_H^{2n+1}$ , n = 1, 2, . . . , in terms of bigraded symplectic structures on the tori T²ⁿ, the corresponding \({\mathfrak{s}\mathfrak{l}}_{2}\) ${\mathfrak{s}\mathfrak{l}}_2$ -representations on the cohomology of T²ⁿ, and the Buchstaber spectral sequence (Bss).