Generalized Bernstein-Reznikov integrals

Jean-Louis Clerc (1) , Toshiyuki Kobayashi , Bent Ørsted , Michael Pevzner (2)

1 IECN - Institut Élie Cartan de Nancy
2 LMR - Laboratoire de Mathématiques de Reims

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.

Domaines: Analyse classique [math.CA]; Théorie des représentations [math.RT]

Jean-Louis Clerc, Toshiyuki Kobayashi, Bent Ørsted, Michael Pevzner. Generalized Bernstein-Reznikov integrals. Mathematische Annalen, 2011, 349 (2), pp.395-431. ⟨10.1007/s00208-010-0516-4⟩. ⟨hal-00400082⟩