All Questions
10 questions
2
votes
1
answer
94
views
Unitary dual of universal cover
The universal covering group $G$ of $\mathrm{SL}_2({\mathbb R})$ has infinite center. Is there an irreducible unitary representation $\pi$ of $G$, whose central character is injective? Or does every $\...
user473423
2
votes
0
answers
228
views
Irreducible group representation(algebraic and topological irreducibility)
In page 280 of "C^* algebra" by Dixmier, in the context of group representation, it is written 'We never encounter the concept of algebraic irreducibility except in finite dimensional ...
- 356
9
votes
1
answer
434
views
Questions on the group $\mathrm{GL}(H)$
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\U{U}$Let $H$ be an infinite dimensional complex Hilbert space. Consider the group $\GL(H)$ of bounded invertible operators on $H$.
Question 1. I've ...
- 1,586
7
votes
1
answer
201
views
Unitary representation is strictly continuous
Let $G$ be a compact group and $u: G \to B(H)$ be a strongly continuous unitary representation on the Hilbert space $H$. Then is $u: G \to B(H)$ strictly continuous?
That is, give $B(H)$ the topology ...
user167952
3
votes
0
answers
141
views
Existence of a unique cyclic and separating vector in a *-representation
I'm interested in knowing the requirements for a $*$-representation, $\pi_{\omega}$, of a C*-algebra, $\mathbb{C}(\mathcal{G})$, (or equivalently the requirements for the unitary representation, $U_{\...
- 31
3
votes
0
answers
237
views
Orthogonality relations for unitary representations of infinite (finitely generated) groups
Let $G$ be a group, and consider the matrix elements of finite dimensional irreducible unitary representations of $G$ over $\mathbb{C}$ as functions $f:G\to \mathbb{C}$. If $G$ is finite, any two ...
- 333
11
votes
2
answers
537
views
Groups without property (T) but all finite quotients are expanders
What is an example of a group $G$ which
1- is finitely generated by $S$,
2- does not have property (T),
3- admits infinitely many finite quotients which do not factor through an homomorphism $G \...
- 4,422
5
votes
0
answers
321
views
Unitary representations of Tarski Monsters and other beasts
Did people study the unitary representations of Tarsky Monsters, for example the ones constructed by Ol'shanskii? Are there any exotic representations, ie. except the ones related to the left regular, ...
- 647
6
votes
0
answers
502
views
Faithful and weakly-mixing representations of Property (T) groups in relation to left regular rep
Is it known that: Any countable Property (T) group (or more generally, a non-amenable group) has a faithful, weakly-mixing representation which is NOT weakly included in its left regular ...
- 647
18
votes
2
answers
1k
views
Regarding Cayley Graphs of Property (T) Groups
A well-known application of Kazhdan's Property (T) is the construction of expander graphs. Background on this is discussed, for example, in this post on Terry Tao's blog. Essentially, Cayley graphs of ...
- 7,047