Let p be a prime and let $\mathbb Z_p$ denote the p-adic integers.
If n<m, then what are the embeddings $SL_n(\mathbb Z_p)\rightarrow SL_m(\mathbb Z_p)$? I am particularly interested in those which carry $SL_n(\mathbb Z)$ into $SL_m(\mathbb Z)$.
There are obvious "block" embeddings, e.g., carrying a matrix to the upper-left hand corner of a larger matrix. There are also certain conjugates of these. In general, the embeddings should come from representations of $SL_n(\mathbb Z_p)$, but I do not know where they are catalogued or what exactly to do with the catalog.