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Results tagged with lie-groups
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user 2365
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
7
votes
1
answer
715
views
Generalization of Rigid Body Motion to arbitrary (compact) Lie Groups
The classical dynamics of a rigid body in three dimensions may be described as the motion of a point on a configuration space given by the Lie group $SO(3)$, governed by Euler's equations for rigid bo …
- 965
10
votes
2
answers
667
views
SO(p,q) and Howe Duality
I recently learned of a relationship between the representations of the groups $SO(p,q)$ and $SL(2,\mathbb{R})$ which is part of an apparently much larger set of ideas known as Howe Duality. My quest …
- 1,141
12
votes
1
answer
2k
views
unitary irreps of O(p,q)
I am interested in the irreducible unitary representations of the orthogonal groups $O(p,q)$. By $O(p,q)$ I mean the real Lie groups which preserve the quadratic form of signature $(p,q)$ in $\mathbb …
- 2,449