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F. C.
F. C.
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Let $p$ be a prime and let $\mathbb Z_p$ denote the p$p$-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.

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.

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.

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edit approved Jan 9, 2020 at 20:41
Alejandro Tolcachier
edit approved Jan 9, 2020 at 20:41
Alejandro Tolcachier
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Embeddings between p$p$-adic linear groups?

Let p$p$ 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.

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.

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.

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Samuel Coskey
Samuel Coskey
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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.