1
vote
0answers
103 views

Do the irreducible unitary representations of a locally compact group form a separating set for the Radon measures on the group?

Let $\mu$ and $\nu$ be two Radon measures on a locally compact group $G$. For every irreducible unitary representation $\pi$ of $G$ and vectors $u$ and $v$ from the corresponding Hilbert space $H_\pi$ ...
6
votes
2answers
131 views

Spherical functions for sl(2,Q_p)

I kindly would like to ask you the following- I am refering to page 175 in the Book by Gelfand, Graev, Shapiro, etc, on "Automorphic forms ..." My question to which I would kindly ask you to answer ...
8
votes
0answers
179 views

when do norm-continuous unitary representations separate points of a group?

Recently I found in the web a discussion on the following question: ...
10
votes
3answers
358 views

Topology on the Unitary Dual

Suppose I have a locally compact topological group G. The unitary dual of G is the set of equivalence classes of irreducible unitary representations of G. Now, it seems to me that the sensible way of ...
6
votes
2answers
220 views

Structure of the unitary representation $L^2(N/M)$ when $N$ is a nilpotent Lie group

Hi All, I am new to this (though I seem to be a latecomer); so forgive me if this is not your most favorite question: I am trying to understand the structure (e.g., decomposition) of the unitary ...
12
votes
3answers
1k views

Positive definite function zoo

I've asked the following question on math.stackexchange but there has been no response so I'll ask it again here: A positive definite function $\varphi: G \rightarrow \mathbb{C}$ on a group $G$ is a ...
7
votes
2answers
569 views

Decomposing an arbitrary unitary representation of a connected nilpotent Lie group in terms of its irreps

For a locally compact (Hausdorff) abelian group $G$ we have following theorem (see e.g. Folland): "For every (strongly continuous) unitary representation $(\pi,\mathcal{H_{\pi}})$ of $G$, there ...
2
votes
3answers
601 views

Plancherel formula for special linear group

I am looking for a comprehensible material covering Plancherel formula for $SL(n,\mathbb{R})$ and $SL(n,\mathbb{C})$. Of course, I wouldn't mind reading an explanation for general semisimple Lie ...
0
votes
0answers
236 views

faithful representation of locally compact group

I have been thinking about existence of faithful representation of locally compact groups. This representation exists for example for compact lie groups. But I am curious to know if one can say some ...