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Results tagged with rt.representation-theory
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user 2164
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
8
votes
Accepted
Can every parabolic subgroup be conjugated to its opposite by an element of the Weyl group?
If I understood your question correct, then the answer is no. I will assume for simplicity that you are talking about parabolic subgroups of complex simple Lie groups. Then your question translates to …
- 1,050
8
votes
1
answer
1k
views
Complex Lie group without faithful real representations?
Does there exist a complex analytic Lie group which doesn't have faithful representations in $GL(N,\mathbb R)$, viewed as a real Lie group?
There are examples of complex Lie groups which do not allow …
- 1,050
21
votes
2
answers
3k
views
Is every finite-dimensional Lie algebra the Lie algebra of a closed linear Lie group?
This question is closely related to this one.
Ado's theorem states that given a finite-dimensional Lie algebra $\mathfrak g$, there exists a faithful representation $\rho\colon\mathfrak g \to \mathfr …
- 1,050
5
votes
2
answers
740
views
explicit linear representations of fundamental groups of surfaces
I am looking for an explicit representation of the fundamental group of a closed orientable surface of genus >1. I guess they should be abundant in degree 2. Did anyone see the explicit matrix constru …
- 1,050