All Questions
7 questions
11
votes
1
answer
2k
views
On unramified p-adic groups
Let G be a reductive group over a local field F. Let O be the ring of integers of F.
The following are equivalent (and groups satisfying these conditions are called unramified):
(a) G is quasisplit ...
- 8,866
9
votes
1
answer
617
views
Characters of simply connected semsimple algebraic groups over local fields
Let $G$ be a semisimple algebraic group over $\mathbb{Q}_p$. Then by definition $G$ admits no non-trivial algebraic characters, i.e. homomorphisms $G \to \mathbb{G}_m$.
However, it is quite possible ...
- 21.4k
8
votes
2
answers
1k
views
Examples to keep in mind while reading the book 'The Admissible Dual...' by Bushnell and Kutzko and the importance of Interwining of representations
I am a beginner in the field of representation theory. I was reading the book 'The Admissible Dual of $GL(N)$ Via Compact Open Subgroups' by Bushnell and Kutzko.
Let me first describe the book a ...
- 685
3
votes
0
answers
168
views
The left regular representation of the Jacobi groups over local fields of characteristic >2 is type I?
Let $K$ be a non-archimedean local field of characteristic $>2$. Consider the Jacobi group $G=H_{2n+1}(K)\rtimes Sp_{2n}(K)$, which is the semidirect product of the Heisenberg group $H_{2n+1}(K)$ ...
- 1,702
3
votes
0
answers
224
views
Metaplectic groups over non-archimedean local fields of characteristic>2
Let $K$ be a non-archimedean local field of characteristic $>2$. Consider the double cover metaplectic extension of symplectic groups
$p: Mp_{2n}(K)\rightarrow Sp_{2n}(...
- 1,702
2
votes
0
answers
415
views
Algebraic characters and quasi-characters of reductive algebraic group over non-archimedean local field
Let $G$ be a reductive algebraic group over $F$, where $F$ is a non-archimedean local field.
Then $G(F)$ is a p-adic group.
Let $\Psi(G)$ be the lattice of algebraic characters.
Let $\Lambda_G$ be the ...
- 1,457
0
votes
0
answers
138
views
Orbits of some action of SL2 on Pontryagin dual of the field of formal Laurent series
Let $K=\mathbb{F}_2((t))$ be the field of formal Laurent series over the finite field $\mathbb{F}_2$. Now consider $K^3$ as an additive group and its dual group $\hat{K^3}$, which consists of all ...
- 1,702