# Tagged Questions

**4**

votes

**1**answer

108 views

### Action of the isometry group of the hyperbolic 5-space

We can think hyperbolic 5-space as, $$\mathcal{H}^5=SO^+_{5,1}(\mathbb{R})/SO_5(\mathbb{R})=SL_2(\mathbb{H})/Sp^*_2(\mathbb{H}),$$$\mathbb{H}$ is real quaternion algebra. By Iwasawa Decomposition the ...

**4**

votes

**1**answer

110 views

### Connection between degree of growth and return probabilities of random walks on Lie groups

Let $G$ be a finitely generated group of polynomial growth, let $\mu$ be a non-degenerate symmetric probability measure with finite support on $G$, and let $d$ be the degree of growth of $G$. ...

**12**

votes

**3**answers

756 views

### How can I tell if a group is linear?

The basic question is in the title, but I am interested in both necessary and sufficient conditions.
I know the Tits' alternative and Malcev's result that finitely generated linear groups are ...

**10**

votes

**0**answers

501 views

### Definition of a uniformly bounded dual of a group

The unitary dual of a group $G$ is the set of equivalence classes of irreducible unitary representations of $G$ with the Fell topology. (This topology is defined using convergence of positive definite ...

**1**

vote

**2**answers

329 views

### Abstract Commensurator Group of $\mathbb{Z}^n$ $Comm(\mathbb{Z}^n)\cong GL(n,\mathbb{Q})$?

Hello! In a paper I read that $\mathrm{Comm}(\mathbb{Z}^n)\cong \mathrm{GL}(n,\mathbb{Q})$. Why is that true? How can I find an isomorphism of this groups?
I know that ...