# Tagged Questions

**2**

votes

**1**answer

192 views

### An upper bound for the maximal subgroups at fixed index?

Let us call a subgroup an injective homomorphism between groups.
I warn the reader that a subgroup designates here an inclusion $(H \subset G)$, not $H$ alone.
A subgroup $H \subset G$ is ...

**11**

votes

**3**answers

1k views

### Is there a purely group-theoretic reformulation of an equivalence of subgroups?

There is an equivalence relation between inclusion of finite groups coming from the world of subfactors:
Definition: $(H_{1} \subset G_{1}) \sim(H_{2} \subset G_{2})$ if $(R^{G_{1}} \subset ...

**7**

votes

**3**answers

503 views

### Compact subgroups of the unitary group of operators in a hilbert space

Is there a characterization for the compact subgroups of the unitary operators in a Hilbert space, where the unitaries are furnished with the norm topology? What about other topologies?

**1**

vote

**0**answers

194 views

### How to correctly name “irreducible subrepresentation of an indecomposable representation”

I am studying the representation theory of some infinite dimensional algebras, for example infinite dimensional Lie-algebras, Kac-Moody algebras, W-algebras. These algebras arise as symmetry algebras ...

**4**

votes

**1**answer

189 views

### Well defined Tensoring of spectral triples

Hi,
I have a misunderstanding that I am hoping is really quite trivial. I will give my question directly and context below for those that need/want it.
Question: In connes standard model he takes ...

**9**

votes

**1**answer

213 views

### Is there a Dedekind-Frobenius group determinant for infinite groups?

If $G$ is a finite group and $\lbrace x_{g} \rbrace_{g\in G}$ are commuting formal variables, then one can form a matrix whose $(g,h)$ entry is $x_{gh^{-1}}$. The determinant of this matrix is a ...

**8**

votes

**2**answers

366 views

### Dimensions of unitary representations of group extensions

Is the property of having a bound on the dimensions of irreducible representations preserved by an extension?
For example $G_1=\mathbb{Z}$ and $G_2=\mathbb{Z}/2\mathbb{Z}$ are discrete abelian ...

**13**

votes

**2**answers

771 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 ...

**5**

votes

**2**answers

281 views

### Induction theorems for finite-dimensional complex representations of infinite groups

Let $G$ be a group, usually infinite. I am interested in finite-dimensional complex unitary representations of $G$, i.e. group homomorphisms $G \rightarrow U_n(\mathbb{C})$. The category of these ...

**10**

votes

**0**answers

270 views

### Can we find arbitrarily many elements of SU(2) generating a good copy of MAX($\ell_1^n$) inside VN(SU(2))?

In trying to prove that the answer to the title is "no", I was led to the following problem (which I think is equivalent to the question asked in the title, but can be stated independently). If ...

**3**

votes

**1**answer

331 views

### injective tensor norms for real tensors

If $A$ is an element of $\mathbb{R}^n \otimes\mathbb{R}^n \otimes\mathbb{R}^n$, then define its injective tensor norm to be
$$\|A\|_{\rm inj} := \max_{x,y,z\in \mathbb{R}^n, \|x\|=\|y\|=\|z\|=1}
...

**0**

votes

**0**answers

165 views

### Characterization of Complex Group Algebras

Is there a way to characterize which complex algebras arise as the group algebra of some locally compact group? To make this more concrete, say $A$ is a sub-algebra of $\text{Mat}(n,\mathbb{C})$, ...

**3**

votes

**1**answer

278 views

### Classification of representations of CCR algebras?

Hi,
I'm wondering if there is a some classification of representations of CCR algebras (http://en.wikipedia.org/wiki/CCR_algebra), where say the underlying vector space is a separable Hilbert space. ...