Yes, "represent firms" in this context likely means that the respondents are representatives or representatives of firms (e.g. asset management companies) and manage assets on behalf of those firms. The $12 trillion to $15 trillion in assets that are mentioned are the assets that are managed by the firms that the respondents represent, rather than the assets that the respondents directly manage themselves.

means the Member who is designated to act as the representative of the Firm in accordance with the Regulations. If someone such as a lawyer or a politician represents a person or group of people, they act on behalf of that person or group.

I don't think this means that the respondents are representative or agents

constitute; amount to.
"this figure represents eleven per cent of the company's total sales"

I think it is meaning 11 below:


represent
1 of 2
verb (1)
rep·​re·​sent ˌre-pri-ˈzent
represented; representing; represents
Synonyms of represent

transitive verb
1: to bring clearly before the mind : present
a book which represents the character of early America
2: to serve as a sign or symbol of
the flag represents our country
3: to portray or exhibit in art : depict
4: to serve as the counterpart or image of : typify
a movie hero who represents the ideals of the culture
5a
: to produce on the stage
b: to act the part or role of
6a(1)
: to take the place of in some respect
(2) to act in the place of or for usually by legal right
(3): to manage the legal and business affairs of
athletes represented by top lawyers and agents
b: to serve especially in a legislative body by delegated authority usually resulting from election
7: to describe as having a specified character or quality
represents himself as a friend
8a: to give one's impression and judgment of : state in a manner intended to affect action or judgment
b: to point out in protest or remonstrance
9: to serve as a specimen, example, or instance of
10a: to form an image or representation of in the mind
b(1): to apprehend (an object) by means of an idea
(2): to recall in memory
11: to correspond to in essence : constitute

https://www.merriam-webster.com/dictionary/represent

Collectively, these respondents directly manage more than $500 billion in assets and represent firms that manage $12 trillion to $15 trillion in assets.
=
Collectively, these respondents directly manage more than $500 billion in assets and form a sample taken from firms (where they work) that manage $12 trillion to $15 trillion in assets.

IOW

they "represent" these firms in the sense that their opinions are a "representative sample" of the ways of thinking of all the assets managers working in these firms:

the respondent themselves manage more than $500 billion, but what they have to say illustrates the ways of thinking of firms that manage $12 trillion to $15 trillion

https://www.investopedia.com/terms/r/representative-sample.a...

They are not any kind of "legal representatives", they "represent" the firms where they work in the same way that around 2000 people answering a voting intention survey would "represent" the whole 47-odd million UK electorate. (yes, that's right no more than 2 thousand people is enough to predict fairly accurately what 47 million people will do)