Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with rt.representation-theory
Search options not deleted
user 1384
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
2
votes
what information of a representation was killed by Jacquet functor?
EDIT: I assumed the OP was asking about reductive groups over non-arch local fields. Emerton raises the possibility that the question is actually about groups over R or C, and he's probably right. So …
- 40.3k
19
votes
2
answers
2k
views
Clifford theory: behaviour of a very general irreducible representation under restriction to...
Let $G$ be a group and let $H$ be a subgroup of finite index.
Let $V$ be an irreducible complex representation of $G$ (no topology or anything: $V$ is just a non-zero complex vector space with a line …
- 40.3k
41
votes
Character table does not determine group Vs Tannaka duality
Let me try and give as low-level an explanation as I can, in case you're scared of all this "monoidal category" stuff.
A complex representation of a finite group $G$ is just a module for the group ri …
- 40.3k
14
votes
Accepted
Any finite dimensional admissible(smooth) irreducible representation of GL(2,Q_p) is 1-dim
What does "admissible" mean for you? Does it imply smoothness (stabilisers are open)? If not then I think the statement might be false (choose some hopelessly discontinuous injection from $\mathbf{Q}_ …
- 40.3k
11
votes
3
answers
1k
views
Version of Brauer-Nesbitt for summands
The Brauer-Nesbitt theorem (well, one of them) says that if $k$ is a field and I have two semisimple representations (on finite-dimensional $k$-vector spaces) $r_1$ and $r_2$ of a $k$-algebra $A$ with …
- 40.3k
3
votes
Version of Brauer-Nesbitt for summands
By a weird coincidence I've found the answer to my question. I was trying to generalise some ideas of Chenevier; I was reading his Jacquet-Langlands paper---a version I'd got from his website. For oth …
- 40.3k
9
votes
Accepted
Are complex semisimple Lie groups matrix groups?
As requested by Faisal, I am posting as an answer the observation that if $G$ has more components than the size of the complex numbers then G has no faithful finite-dimensional irreducible representat …
- 40.3k
19
votes
Accepted
When do the sizes of conjugacy classes and squares of degrees of irreps give the same partit...
My standard rant about "what can we say about $G$": what we can say about $G$ is that the two partitions are the same. If the questioner doesn't find that a helpful answer then they might want to cons …
- 40.3k
4
votes
SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)
If you think about this question in terms of automorphic representations then it sort of becomes trivial. The space $Sk(\Gamma(N))$ can be re-interpreted as the direct sum of $\pi^{U(N)}$, where $\pi$ …
- 40.3k
9
votes
4
answers
992
views
Structure of cuspidal Bernstein components—do non-commutative endomorphism rings ever really...
Let $F$ be a finite extension of $\mathbf{Q}_p$ with integers $\mathscr{O}$, let $\mathbb{G}$ be a connected reductive group over $F$ and let $G=\mathbb{G}(F)$ be its $F$-points. Let $X(G)=\operatorna …
- 40.3k
6
votes
Accepted
Finite dimensional automorphic representations of a definite quaternion with prime discrimin...
1) Yes, I think that's true. I guess it follows relatively easy from the statement that an automorphic representation of the algebraic group $D^\times$ is finite-dimensional iff it's 1-dimensional and …
- 40.3k
4
votes
1
answer
450
views
Injection between non-isomorphic irreducible Hilbert space reps?
I must be missing something trivial here.
Let $G$ be, say, a reductive Lie group (or more generally any locally compact Hausdorff unimodular topological group). A unitary Hilbert space representation …
- 40.3k
11
votes
1
answer
1k
views
Extension of induced reps over Z: is it a sum of induced reps?
Let $G$ be a finite group. If $L$ is a finite free $\mathbf{Z}$-module with an action of $G$, say $L$ is induced if it's isomorphic as a $G$-module to $Ind_H^G(\mathbf{Z})$ with $H$ a subgroup of $G$ …
- 40.3k
8
votes
3
answers
982
views
When does a unitary Hilbert space rep of a reductive Lie group decompose into a direct sum o...
I'm giving some lectures on the trace formula. Here's something I proved in the last lecture. Let $G$ be a locally compact Hausdorff unimodular topological group (e.g. a reductive Lie group), let $\Ga …
- 40.3k
29
votes
5
answers
2k
views
Does $S_4$ inject into $SL(2,R)$ for some commutative ring $R$?
$\newcommand{\Z}{\mathbf{Z}}$
Given a nice infinite collection of groups, for example the symmetric groups, one can ask whether any finite group is a subgroup of one of them. Of course any finite grou …
- 40.3k
19
votes
2
answers
2k
views
Uniqueness of local Langlands correspondence for connected reductive groups over real/comple...
In Langlands' notes "On the classification of irreducible representations of real algebraic groups", available at the Langlands Digital Archive page here, Langlands gives a construction which is now r …
- 40.3k
18
votes
6
answers
2k
views
Explicit formula for the trace of an unramified principal series representation of $GL(n,K)$...
Let $K$ be a non-arch local field (I'm only interested in the char 0 case), let $\mathbb{G}$ be a connected reductive group over $K$ and let $G=\mathbb{G}(K)$. If $V$ is a smooth irreducible complex r …
- 40.3k
11
votes
1
answer
1k
views
Simple explicit example of local Jacquet-Langlands theorem for inner forms of GL(n), and con...
This one will be very easy for the experts.
Let $F$ be a nonarch local field, let $n\geq1$ be an integer, choose $0\leq d<n$ and let $D$ be the central simple algebra over $F$ with invariant $d/n$ in …
- 40.3k
13
votes
Definition of L-function attached to automorphic representation
I think you're slightly misled. $\pi$ doesn't have an $L$-function "in abstracta". An unramified $\pi_v$ at a finite place $v$ gives rise, by Langlands' interpretation of the Satake isomorphism, to a …
- 40.3k
46
votes
Accepted
Are there Maass forms where the expected Galois representation is $\ell$-adic?
Here's some piece of the bigger picture. Maass forms and holomorphic modular forms are both automorphic representations for $GL(2)$ over the rationals. An automorphic representation is a typically hug …
- 40.3k
28
votes
Accepted
What's the point of a Whittaker model?
This question is a bit like saying "what's the point of the theory of bases for vector spaces -- this just gives you an isomorphism of your space with $\mathbb{R}^n$. What is the point of defining thi …
- 40.3k