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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

12 votes
3 answers
2k views

What is a good introduction to branching rules in representation theory?

I'm looking for a book or introductory article, that explains branching rules in representation theory of real Lie groups. When a Lie group has a set of irreducible representations, I'd like to know h …
Manuel Bärenz's user avatar
4 votes
1 answer
1k views

When are induction and coinduction of representations of Lie groups isomorphic? When they ar...

This is in a sense a follow up on the popular question Induction and Coinduction of Representations, where this particular question is one of several points, and it is neglected. It seems that the re …
Manuel Bärenz's user avatar
0 votes
Accepted

From the representation category of a Lie group and the representation on a homogeneous spac...

I understand it for finite groups now, and I suspect that it's similar for semisimple Lie groups. These statements are equivalent, and true for finite groups: The adjunction $\operatorname{Res} \da …
Manuel Bärenz's user avatar
2 votes
1 answer
260 views

From the representation category of a Lie group and the representation on a homogeneous spac...

Given a Lie group $G$ and a transitive action $- \triangleright - : G \times X \to X$ on a homogeneous space, we can recover the stabiliser subgroup $H_x$ of a point $x \in X$. It is the subgroup of $ …
Manuel Bärenz's user avatar