All Questions
Tagged with p-adic-numbers rt.representation-theory
6 questions
4
votes
1
answer
239
views
A specific $2$-dimensional Galois representation of $G_{\mathbb{Q}_2}$ and its Langlands correspondence
I am interested in understanding a situation in (classical, not $p$-adic) local Langlands for $\mathrm{GL}_p(\mathbb{Q}_p)$. An example of
it is as follows: Let $F=\mathbb{Q}_2$ and $E$ be the ...
- 1,856
0
votes
0
answers
81
views
Can every $\ast$-algebra be represented in this space of matrices?
Let $k$ be a field with characteristic $0$. For every set $X$, let $\mathcal{B}(X)$ be the set of (possibly infinite) matrices $T = (T_{x,y})_{x,y \in X}$ with coefficients in $k$ such that in each ...
- 1,485
1
vote
1
answer
150
views
Quadratic unramified extension of a p-adic field
Let $F$ be a non-archimedean local field of residual characteristic $p\neq 2$, and let $E=F[\sqrt{\epsilon}]$ be the quadractic unramified extension, here $\epsilon$ is a non-square element of $\...
- 63
4
votes
0
answers
306
views
Computing the $2$-adic volume of a special orthogonal group
Let $n \geq 0$ be an integer, let $A = (a_{ij})$ be the $(2n+1) \times (2n+1)$ matrix defined by $a_{ij} = 0$ unless $i + j = 2n+2$, in which case $a_{ij} = 1$. Let $G$ be the group scheme over $\...
4
votes
0
answers
124
views
Finite dimensional irreps of $p$-adic groups
What are some examples of finite dimensional irreducible complex representations of $SL_2(\mathbb{Q}_p)$?
One knows such a representations cannot be smooth, so probably the examples will be ...
- 81
1
vote
1
answer
881
views
Why is every l-adic Galois representation conjugate to one over the l-adic integers? [closed]
Why is every l-adic Galois representation
$$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Q}_{l})$$
conjugate to one over the l-adic integers?
$$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Z}_{l})$$
- 1,805