# Tagged Questions

**5**

votes

**3**answers

306 views

### Decomposition of $L^2(\Gamma \backslash G)$

Let $G$ be a semisimple Lie group, and $\Gamma$ be an lattice (arithmetic) - typical examples I am thinking about would be $(SL_2(\mathbb{R}), SL_2(\mathbb{Z})$, or $(SL_2(\mathbb{C}), PGL_2(O_F))$ ...

**5**

votes

**0**answers

132 views

### Which cocompact subgroups of $G$ do contain a cocompact normal subgroup of $G$?

Let $G$ be a locally compact group and let $H$ be a cocompact (or more generally, a cofinite) subgroup of $G$.
Is there any criterion to determine whether $H$ contains a cocompact normal subgroup of ...

**4**

votes

**2**answers

251 views

### “geometric” description of the algebra of central functions on a Lie group

I am looking for a a description of the algebra of continuous central functions on a group, say a compact simple Lie group $G$, as the algebra of all continuous functions on a "nice" compact Hausdorff ...

**2**

votes

**1**answer

251 views

### Characters separating points on Maximal Torus modulo Weyl group?

Let G be a compact Lie group, for example, SU(n). Let T be its maximal torus. Let W be its Weyl group.
Every finite-dimensional representation of G has a character, which is a function on G, T and ...

**6**

votes

**2**answers

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 ...

**4**

votes

**1**answer

386 views

### Can one understand the Kelvin transform conceptually?

Let $U = \mathbf{R}^n - \{ 0 \}$, $n > 2$ and consider for a function $f \in C^2(U)$ the Kelvin transform
$$f^\star(x) = r^{2-n} f\left(\frac{x}{r^2}\right),$$
where $r = \lvert x \rvert$. One ...

**1**

vote

**1**answer

127 views

### Dominant weights appear in Discrete Series

If $\lambda$ is a Harish-Chandra paramater. Let $\pi_\lambda$ it's associated discrete series, it's known by the minimal K-type thm that every K-type of $\pi_\lambda\mid_K$ has highest weight of the ...

**3**

votes

**1**answer

477 views

### Are there explicit formulas for spherical functions on oriented real grassmannians?

Let $p$ and $q$ be integers. The group $K=SO(p) \times SO(q)$ can be naturally seen as a subgroup of $G=SO(p+q)$. The quotient space $G/K$ is identified with the space of oriented $p$-dimensional ...

**15**

votes

**2**answers

777 views

### Borel set plus a closed set = Borel

Hi,
Let $R$ be equipped with the usual Borel structure. Let $F$ be a Borel subset and $E$ be a closed subset of $R$. Then $F+E=(f+e: f\in F, e \in E \)$ is Borel? If yes, is it true for any locally ...