Are non-equivalent irreps with dimension n of a lie algebra share the same weight set? E.g. in su(2), given a dimension of the irrep, the weight set is the same no matter what exactly the irrep is. Is it generally true for any lie algebra?
2026-04-27 22:05:13.1777327513
Are different representations (with the same dimension) of a Lie Algebra share same weights?
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$\mathfrak{su}(2)$ only has a single irrep in each dimension. Anyway, the answer is no: the (multi)set of weights of an irreducible representation of a semisimple (otherwise I don't know what you mean by "weights") Lie algebra completely determines it up to isomorphism.