The concept of representation, people, things.

[shikamaru]

I have been searching for a treatise on "representation" of people, things, etc.

It seem that you must have the ability to think in the "abstract" to comprehend that people can be represented as well as things. Michael Joseph has made excellent points that you must have a fundamental comprehension of trusts, and how trusts are derived from relationships. I think that a to understand relationships, you must also have to be able to understand that you can have a relationship through an agent, and as a principal, that agent represents you.

If you have any leads, please let me know.

The terms 'fungible' and 'fungibility' may lend some clues in to understanding of representation.

Voters, rights, duties, and obligations are all fungible.

To represent someone could also be a party to an agreement or controversy.

A few jural relationships to consider (the list below is not exhaustive):

Principal - Agent
Patron - Client
Master - Slave
Master - Servant
Employee - Employer
Principal - Surety
Obligee - Obligor
Mortgagee - Mortgagor
Promisee - Promisor
Beneficiary - Trustee
Trustee - Trustor

All the above have to do with obligations and duties which can be transferred.
The parties are fungible. That which is fungible is capable of substitution, a placeholder. Substitution is a key element of representation.