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Results tagged with division-algebras
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user 56638
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 …
- 255
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 $SL_1(D)$ …
- 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 …
- 255