bio | website | plusepsilon.de |
---|---|---|
location | Uni Hamburg | |
age | 29 | |
visits | member for | 4 years, 5 months |
seen | Jan 31 at 13:20 | |
stats | profile views | 8,457 |
Mar 24 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
@Marty I thought more about your claim about the intertwiner. You can see that JL are using the one that I describe as does Bump, etc. By Schur's lemma, there can be only one intertwiner up to a constant. It is the standard one for the adelic Eisenstein series as well. Yours does not match up with the standard one times a constant, or does it? |
Mar 24 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
You get one quotient and one submodule, so yes that makes too. But the roles are interchanged in $I(\mu)$ and $I(\mu^w)$. |
Mar 23 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
Are you sure? I can't see the invariance. The integral transfer needs to map $I(\mu)$ to $I(\mu^w)$. |
Mar 22 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
Also there are other references for SL(2,C). Knapps book on semisimple groups or Wallachs book on reductive groups. Wallach seems more informative concerning things like temperedness and unitarity. SL(2,C) and GL(2,C) are very similar, not like SL(2,R) and GL(2,R). |
Mar 22 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
I have chosen to delete my answer, because it seems not to address your question. As Marty points out $I(\chi_1,\chi_2)$ is isomorphic to $I(\chi_2,\chi_1)$ if both are irreducible. If they are reducible, they are not. What is an irreducible subquotient in one of them is an irreducible subrepresentation in the other. So that's why considering only unique subquotients hits all irr reps. |
Mar 22 |
comment |
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
The intertwiner seems wrong. You need $\int\limits_{U} f(wux) du$ for $w$ the Weyl element, or not? |
Mar 21 |
awarded | Custodian |
Mar 21 |
reviewed | Approve phase portrait of system of differential equations |
Mar 20 |
comment |
The representation of a group
What kind of maps? Group homomorphisms, I guess? |
Mar 20 |
comment |
reference help about a result on representation theory
Ah okay, I see imaginary line modulo $x=2 \pi i / log(q)$, $q$ being the residue characteristic, that's isomorphic to $U(1)$, I guess:) I didn't see that before:\ But that's a confusing embedding of $U(1)$ into $\mathbb{C}^\times$ modulo $x$. |
Mar 20 |
comment |
reference help about a result on representation theory
@WillSawin My issue is that unitary one-dimensional representation live on the imaginary line, not $U(1)$. |
Mar 20 |
comment |
Simultaneously extending the functionals of a subspace of a Banach space to the whole space
Be careful, there exists Banach spaces which do not admit a Schauder Basis. The first examples are due to Enflo. |
Mar 20 |
comment |
Simultaneously extending the functionals of a subspace of a Banach space to the whole space
There are results available, when the extension is unique, e.g. in a Hilbert space or more general results can be found here jstor.org/discover/10.2307/…. Of course, Hamel basis are not to be chosen in topological vector space, e.g. for Banach spaces one works with a Schauder basis. |
Mar 20 |
revised |
reference help about a result on representation theory
added 1 characters in body |
Mar 20 |
revised |
reference help about a result on representation theory
added 25 characters in body |
Mar 20 |
revised |
reference help about a result on representation theory
added 25 characters in body |
Mar 20 |
answered | reference help about a result on representation theory |
Mar 16 |
comment |
What can the theory of automorphic forms for $SL(n,\mathbb{Z})$ say about $SL(n,\mathbb{Z})$?
There is no Eichler-Selberg type trace formula for SL(3) because of the abscence of discrete series for SL(3,R). |
Mar 16 |
comment |
What can the theory of automorphic forms for $SL(n,\mathbb{Z})$ say about $SL(n,\mathbb{Z})$?
there are certainly not easy ways to study this rep.theory... I meant to say easier ways in my last comment:\ |
Mar 16 |
comment |
How can I find the spectrum of this operator?
Pls use one/two dollar signs for math |