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Results tagged with rt.representation-theory
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user 50929
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
6
votes
1
answer
135
views
Does the centralizer of a regular element in a semisimple Lie algebra act by polynomials?
Let $\mathfrak g$ be a semisimple Lie algebra over $\mathbb C$, $\rho : \mathfrak g \to \operatorname{End}(V)$ a finite-dimensional irreducible representation and $x \in \mathfrak g$ regular with cent …
- 348
6
votes
Accepted
Does the centralizer of a regular element in a semisimple Lie algebra act by polynomials?
It is false for the same reason the first example is wrong. Take $\rho$ for example the adjoint representation. As soon as $\mathfrak g$ has rank at least $2$ you can find a regular semisimple $x$ suc …
- 348