They might seem interchangeable. However, I found their definitions in Law.com on "represent" and "on behalf of" (delegate)

represent
v. 1) to act as the agent for another. 2) to act as a client's attorney. 3) to state something as a fact, such as "I tell you this horse is only four years old." 4) to allege a fact in court, as "I represent to the court that we will present six witnesses," "We represent that this is the final contract between the parties."
See also: representation

delegate
1) v. to assign authority to another. 2) n. a person chosen to attend a convention, conference or meeting on behalf of an organization, constituency, interest group or business.