In Pride and Prejudice by Jane Austen, how does Pemberley represent Mr. Darcy?
Supposing that "represent" in this context means something different from "symbolize," using the definition of "represent" that is "to stand as an equivalent of; correspond to" (Collins Dictionary), let's explore what is known of Pemberley to determine how Pemberley might represent Darcy.
It is known from Elizabeth's visit to Pemberley that it is a great, imposing house and estate of woods that all the associated townspeople are respectful of, speaking well of its history and beauty, as Elizabeth comes to speak, as well:
Elizabeth saw, with admiration of his taste, that it was neither gaudy nor uselessly fine; with less of splendour, and more real elegance.
We know too that the "natural stream" in front of Pemberley House was improved and made greater than its natural "importance" but that this was done with elegance and taste, "without any artificial appearance." We know too that the stream is noted for its fishing as well as for its accommodation to the woodland walker, such as Elizabeth: "a beautiful walk by the side of the water, and every step was bringing forward a nobler fall of ground."
We know from Elizabeth's reactions, as told by the narrator, that every room of Pemberley House had a new vista out onto the great wooded park of the estate. We know too that the park, besides being vast, is varied in its aspect: it has a low point, an ascent of a hill to a "prominence," a small valley, and "high woody hills." We know too that the House is "a large, handsome stone building, standing well on rising ground."
Now the question is, does this, and how does this, represent Mr. Darcy? It appears that Pemberley House is representative of Darcy. Like the house, Darcy is handsome with a strong foundation and morally he stands on metaphorical high ground. Like the park, he has a varied personality and inner character that is difficult to know in just one situation. just one set of circumstances. For instance, at Longbourne, it was not possible for Elizabeth to know that "not one of his tenants or servants but will give him a good name," yet this is true. Elizabeth needed a new "window" from which to look out, from which to see a new perspective.
Also like Pemberley, Darcy is elegant and accommodating to varied interests. While the rooms are elegantly furnished and the grounds are excellent for both fishing and walking, Mr. Darcy is an excellent, brother, landlord, employer and benevolent philanthropist. The conclusion to this exploration is that Pemberley represents Darcy by having the same solid character and generous accommodation that he has. What can be said of Pemberley House and Woods, can be said metaphorically of Darcy. Just as the House has spacious elegant rooms, Darcy has a spacious and elegant spirit that is as strong as the high "ridge" that backs Pemberley House (though Darcy learns to yield some of his rigidity in time).