rt.representation theory - Embeddings between p-adic linear groups?

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.