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8 votes
2 answers
288 views

Representations of $SL_1(D),$ where $D$ a division algebra over a local field

Let $k$ be a local field of residue characteristic $p$, and let D be a central division algebra over $k$ of index $n>2$. How to determine the irreducible complex representations of the group $SL_1(D)$ …
sampath's user avatar
  • 255
3 votes
1 answer
153 views

Idea of base change for Division algebras over local field

Let $F$ be a non-Archimedean local field of characteristic $0$ and $K/F$ be a finite extension. Let $D_F$ be the central division algebra of dimension $n^2$ over $F.$ Write $D_K=D_F\otimes_FK$, which …
sampath's user avatar
  • 255
7 votes
0 answers
492 views

mod $p$ Jacquet-Langlands correspondence

Let $F$ be a local field of characteristic $0$. Let $D$ be division algebra over $F$ of dimension $n^2$. The construction of irreducible complex representations of $D^*$ is known by Howe, Zink, and ot …
sampath's user avatar
  • 255