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

TL;DR

This paper constructs holographic operators as integral transforms to decompose tensor products of holomorphic function spaces on Hermitian symmetric spaces of tube type into irreducible components, generalizing previous results.

Contribution

It introduces a new integral operator framework for decomposing tensor products of holomorphic function spaces on Hermitian symmetric spaces of tube type.

Findings

Constructed explicit intertwining operators as integral transforms.

Generalized previous results by Kobayashi--Pevzner (2016).

Provides a systematic method for tensor product decomposition.

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 (2016).