1
vote
0answers
31 views

Family of equivalent unitary representations is not a set.

I have recently come across a statement in the book: Kazhdan's property (T) by B. Bekka, P. de la Harpe, A. Valette at the beginning Appendix F.2. Fell topology on sets of unitary representations. ...
3
votes
0answers
44 views

Integration over uncountable set of characters

Let $G$ be a compact (assumed Hausdorff) group and $\hat{G}$ be the set of all characters of irreducible, finite-dimensional representations of $G$. It might occur that $\hat{G}$ is uncountable. It ...
0
votes
0answers
20 views

Properties of characters that remain true for infinite compact groups

Which properties of irreducible characters for finite groups still hold for infinite (compact) groups? In particular, is it still true that the irreducible characters form a basis for the space of ...
0
votes
0answers
17 views

What is the relationship between the spaces $\mathscr K (G)$ and $L^2(G)$?

The context is that $G$ is a locally compact Hausdorff group, $\mathscr K (G)$ is the space of continuous compactly-supported functions $G \to \mathbb C$ equipped with the inner product $(f|g) = \int ...
0
votes
1answer
42 views

A Tensor Product Identification

Hi folks just looking at Timmermann's "Introduction to Quantum Groups and Duality" and looking at the algebra of representative functions on a compact topological group $G$. I take off in Example ...
4
votes
1answer
59 views

reference request: proof that group characters are a basis for $L^2$

I know the following must be very standard, but I haven't found it in any of the functional analysis books to which I have access. Do you know where I can find a self-contained proof?: If $G$ is a ...
3
votes
1answer
68 views

Representation of topological groups

I am looking for a good book of topological representation. I have a very good insight of representation theory of finite groups, and I want to explore topological representations. I saw a book by ...
2
votes
1answer
279 views

Difference between the SU(2) and SO(3) lie groups and their lie algebras

In many places I have seen the SU(2) and SO(3) lie algebras used interchangeably. How are they exactly identical? Moreover, what about their lie groups? Are they identical as well. It would be great ...
4
votes
1answer
134 views

Weil's proof of a theorem on finite irreducible representations of products of compact groups

Theorem Let $G$ and $H$ be compact groups. Let $ρ$ be a finite dimensional irreducible continuous representation of $G×H$ over the field of complex numbers. Then $ρ$ is a tensor product of irreducible ...
1
vote
1answer
61 views

unitary representation and denseness.

I have the next unitary representation, $\pi : G\rightarrow \mathcal{U}(H)$, where G is a closed subgroup of $S_{\infty}$ (the group of bijective functions from $\mathbb{N}\rightarrow \mathbb{N}$), ...