Abstract
We find a closed formula for the triple integral on spheres in \({\mathbb{R}^{2n} \times \mathbb{R}^{2n} \times \mathbb{R}^{2n}}\) whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein–Reznikov integral formula in the n = 1 case. Our method also applies for linear and conformal structures.
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Clerc, JL., Kobayashi, T., Ørsted, B. et al. Generalized Bernstein–Reznikov integrals. Math. Ann. 349, 395–431 (2011). https://doi.org/10.1007/s00208-010-0516-4
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DOI: https://doi.org/10.1007/s00208-010-0516-4