The implicit verb is simply “be”:
Some symbols acquire a multitude of meanings,
some [of which] [are] widely shared [meanings],
others [of which] [are] personal [meanings],
[and] some [of which] [are] contradictory, conflicted, or ambivalent [meanings].
This is a common structure to describe different parts of a subject with different adjectives, while avoiding repetition of the subject or verb. For example:
I bought four apples: two red, two green.
All of these are equivalent:
- I bought four apples: two apples [were] red, two apples [were] green.
- I bought four apples: two red ones, two green ones.
- I bought four apples: two red apples and two green apples.
- I bought four apples. Two of them were red and two of them were green.
Similar yet unrelated to this structure, some adjectives are postpositive, that is, they come after the noun they modify. Examples include: “the best hotel possible”, “the person responsible”, “the town proper”, “the attorney general”. This also appears in poetic language, like “the sky blue and forest green”, or “he called for his fiddlers three”.
Some symbols acquire a multitude of meanings, **as** some of these meanings are widely shared, others are personal, some are contradictory, conflicted, or ambivalent.
The sentence in question can be rephrased using adverbial clauses.