Generalized Bernstein–Reznikov integrals

By J. Clerc, Toshiyuki Kobayashi, B. Ørsted, M. Pevzner. 2009

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a216d40ea5d8eac71657cbe64964ed8e6737552f

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In Applied Mathematics

1. T. Oshima
2. Toshiyuki Kobayashi

In Geometry and Topology

1. T. Matsuki
2. Toshiyuki Kobayashi
3. T. Oshima
4. M. Pevzner

Citations in the corpus

• Finite multiplicity theorems for induction and restriction (2011, background): “The condition (HP) in the triple product pair has laid a solid foundation of concrete analysis of the tensor product of two representations (see [3] for (8)G = SL(2,R); [7] for (8)G = SO(n, 1), for instance).”
• CLASSIFICATION OF FINITE-MULTIPLICITY SYMMETRIC PAIRS (2013, background): “6, a meromorphic family of invariant trilinear forms of principal series representations of the Lorentz group O(n, 1) was studied in [4].”