What particular aspect of America is Erica meant to represent?
I think that Erica is meant to represent that aspect of America that Changez is never meant to obtain. In so many ways, Erica represents the essence of that American Dream which drives Changez. Erica is one that Changez sess as the embodiment of "class," akin to a Gwyneth Paltrow. She comes to represent an ideal, external to Changez's own being, that motivates Changez in his pursuit of the American Dream.
Yet, over time, this pursuit is futile for Changez. Changez's ability to fully immerse himself in Erica's world is impossible for him. There is always a barrier that prevents him from being fully accepted. Erica comes to represent America for Changez. He continually strives for acceptance into something that does not accept him back. Changez tries desperately to be accepted by Erica. Even when he tells her to imagine himself as Chris, her former boyfriend, he is willing to subjugate his own identity. Yet, it is to avail as Changez is not able to find acceptance in Erica, similar to as he feels he is unable to find acceptance in America. When her manuscript contains no mention of Changez, his futility becomes evident. It is here in which Erica and America come to represent the same element for Changez.