The haar-measure tag has no usage guidance.

**9**

votes

**1**answer

182 views

### Haar measurable sets and quotient maps

Let $G$ be a locally compact Hausdorff group with a Haar measure $\mu$, let $H$ be a closed normal subgroup of $G$, and let $q: G \to G/H$ be the quotient homomorphism. Let $\nu$ be a Haar measure ...

**21**

votes

**0**answers

1k views

### Correspondence between eigenvalue distributions of random unitary and random orthogonal matrices

In the course of a physics problem (arXiv:1206.6687), I stumbled on a curious correspondence between the eigenvalue distributions of the matrix product $U\bar{U}$, with $U$ a random unitary matrix and ...

**10**

votes

**0**answers

181 views

### Status of the analog of the Haar measure on quantum groups

In (Masuda, Nakagami, Woronowicz)'s paper, in the introduction, the authors mentioned the deficiency common to both their and (Kusterman, Vaes)'s approach regarding the Haar state (or Haar measure ...

**4**

votes

**0**answers

89 views

### Concentration of measure for uniform distribution on Stiefel manifolds

This is my first post on MO, so I hope the question is suitable. I am looking at the uniform distribution on the Stiefel manifold, but more specifically, at the uniform distribution on the ...

**4**

votes

**0**answers

118 views

### The Haar integral on uniform spaces

Does anybody know what the current research status is on the topic of Haar measures on uniform spaces? I'm specifically interested in compact uniform spaces and its corresponding Haar probability.
As ...

**4**

votes

**0**answers

444 views

### Haar measure on strictly upper triangular matrices

Let F be a function field, and A its adele ring. I want to consider U(A)/U(F), where U(A) is the space of strictly upper triangular matrices with entries from A, and U(F) is the same with entries ...

**3**

votes

**0**answers

377 views

### Haar measure on Galois groups

Galois groups are nice compact Hausdorff groups, and therefore possess a bounded Haar measure, unique if we insist that the total volume be $1$. What is the Haar measure on the absolute Galois group ...

**2**

votes

**0**answers

165 views

### Justification of the convolution operation of $L^1(G)$ functions where $G$ is a LCA group (measurability)

Suppose $G$ is a locally compact abelian Hausdorff group (LCA), and $\lambda$ is the Haar measure on it. We all know the convolution of two $L^1(\lambda)$ functions $f$ and $g$ on $G$ is defined as
...

**2**

votes

**0**answers

128 views

### Chen's iterated integrals and free loop space

I recently found out about Chen's iterated integrals for paths in a differentiable manifold, and I was wondering if an analogous construction exists for free loops, i.e. a set of variables one ...

**2**

votes

**0**answers

130 views

### Almost conjugation-invariant neighborhoods of units in locally compact groups

Let $G$ be a locally compact topological group with unity $e$ and left Haar measure $m$. Let also $g\in G$ be a given element and $U$ a neighborhood (of compact closure) of $e$.
I am interested to ...

**2**

votes

**0**answers

99 views

### Haar Functionals and Coquasi-triangular Structures

In this question it is mentioned that the coordinate algebra $C_q[G]$ Drinfeld--Jimbo algebras, for $G$ a compact semi-simple Lie group, admit a unique positive definite Haar functional. I was ...

**1**

vote

**0**answers

41 views

### Differential of Haar integral function

Let $C^k$ action of a compact Lie group $G$ on $R^m$, $D(g)$ denote the differential of the map $x\in R^m \mapsto g(x) \in R^m$ at the origin and $\mu$ is the normalized Haar mesure on $G$, consider a ...

**1**

vote

**0**answers

185 views

### Question on the Quotient Integral Formula

I have a very concrete question on the proof of the following (see below): Given a 'nice' top. space $X$ and a 'nice' group operation of $G$, say, from the right, on $X$ and a certain measure on $X$, ...

**1**

vote

**0**answers

197 views

### exotic compact group

Let $G$ be compact (and Hausdorff) group, $\mu$ be Haar measure on $G$. Is it always true that $(G,\mu)$ is a standard probability space (Lebesgue-Rokhlin space)? It is so if (a priori not iff) the ...

**0**

votes

**0**answers

38 views

### The use of Haar measure in the Blichfeldt-Minkowski Lemma

I'm trying to understand a proof of the following result
Theorem: Let $K$ be a number field, and $|| \cdot ||$ the idelic norm (product of the normalized absolute values at each place). There ...