Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

TL;DR

This paper investigates the structure of tensor products of tame representations of the infinite unitary group U( ), revealing their invariants and contragredient representations within Fock spaces.

Contribution

It provides a detailed description of tensor product decompositions and invariants for tame representations of U( ), advancing understanding of their algebraic and functional-analytic properties.

Findings

Tensor products of tame representations are explicitly described.

Invariants are realized on Bargmann-Segal-Fock spaces.

Contradient representations are characterized within the same framework.

Abstract

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on Bargmann-Segal-Fock spaces.