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Let $\Gamma_n$ be the $n$-th congruence subgroup of $GL(2,\mathbb{Z}_p)$. So $\Gamma_n$ consists of matrices in $GL(2,\mathbb{Z}_p)$ which are congruent to the identity matrix modulo $p^n$. Let $Z(\...

Consider the very well-known result that any Hermitian matrix over $\mathbb{C}$, say $T$, admits a decomposition $T = UDU^*$ where $U$ is unitary and $D$ is diagonal with real entries. I am looking ...