Holographic operators for the tensor products of the spaces of holomorphic functions on Hermitian symmetric spaces of tube type

Abstract

We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the intertwining operator (holographic operator) from each irreducible summand to the tensor product as an integral operator. This gives a generalization of the result by Kobayashi--Pevzner (2020).