All Questions

What is known about the subgroup $U(n)\subset U(mn)$ for $m,n\in\mathbb{N}$ given by the diagonal embedding $$ \alpha\mapsto \text{diag}(\alpha,\cdots, \alpha),$$ for $\alpha$ appearing $m$ times? For ...

Do we have easily and practically useful quaternion representation for $SU(3)$ group element and for Haar measure? Also, is $SU(2)$ really simplified in the quaternion base?

I understand that there are invariant Haar measure for eigenvalues of unitary matrix. I further understand that absolute value of eigenvalues of unitary matrix is 1. But, I could not find any analysis ...

Consider the group $U(d_1) \otimes U(d_2)$ of "local unitary" operators acting on the complex space $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_2}$ (i.e., $U(d_1) \otimes U(d_2)$ is the group of unitary ...

Consider a separable irreducible unitary representation of $U(\mathcal{H})$ in the Hilbert space $V$. Assume that $\mathcal{H}$ is separable. My question is the following: Is it true that all ...