All Questions

Let $V=\mathbb{R}^n$, $\Lambda_r=2\pi r \mathbb{Z}^n \subset V (r>0)$ a lattice; $V^*\cong\mathbb{R}^n$ the dual vector space of $V$, and $\Lambda_r^*=\frac{1}{2\pi r} \mathbb{Z}^n =\text{Hom}(\...

What are the matrix coefficients associated with the irreducible representations of a compact real linear algebraic group $G$? Peter-Weyl tells us that $L^2(G)$ is the (closure of) $\bigoplus_\pi A_{\...

The motion group of $\mathbb R^2$, noted by $G=M(2)$ is the semi-direct product of $\mathbb R^2$ with the special orthogonal group $K = SO(2)$. A well known fact is that the unitary dual $\hat{G}$, of ...