0
votes
0answers
26 views

$ L^{2} $ convergence should imply convergence in infinity norm

My situation is the following: suppose we have a Lie group $ G=G_{1} \times G_{2} $ and let $ X = \Gamma \backslash G $ a homogeneous space arising from a lattice, i.e. we have a $ G $ invariant ...
0
votes
0answers
11 views

Integrating over a flag manifold

I need to calculate an integral over the flag manifold $U(4)/U(1)\times U(1)\times U(1)\times U(1)=U(4)/T^4$. How can I derive the correct Haar measure to use?
1
vote
1answer
91 views

Itzykson-Zuber integral over orthogonal groups

I would like to know is there a closed form expression for the following Itzykson-Zuber integral for the orthogonal case. $I=\int_{\mathcal{O}(p)} ...
1
vote
0answers
32 views

Integration on associated vector bundle

Let $G$ be a compact lie group and $\mathfrak{g}$ be its Lie algebra then we can construct the integral on $G\times \mathfrak{g}$ by $$\int_G\int_{\mathfrak{g}}f(x,Y)dxdY$$ Where $x\in G$ and $Y\in ...
2
votes
1answer
65 views

decomposition of Haar measure and Fubini theorem

Let $G$ have a unique decomposition $G=AB$, where $G,A,B$ are linear Lie groups with $G,A$ unimodular. Suppose we have Haar measure decomposition $dg=dad_rb$ where $d_rb$ is the right Haar measure on ...
1
vote
0answers
49 views

Performing integration over $U(d)$

Is there any more or less efficient way to integrate a function (not necessarily a polynomial) over $U(d)$?
1
vote
0answers
72 views

Dilation Invariance

Given the formula $$F(x)= \sum_{n=-\infty}^{\infty}f(x+n) $$ We know that is invariant under translations of the form $y=x+n$ for any integer $n$. However can we find a similar formula for dilations ...