Marc Palm
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 Mar 29 revised What is the logarithmic derivative of an (intertwining) operator? added 8 characters in body Mar 29 answered Current Status on Langlands Program Mar 29 comment Current Status on Langlands Program I would also distinguish between functoriality (maps) and correspondence (objects)... you seem to be interested in correspondence between automorphic reps and Galois reps. Mar 29 revised What is the logarithmic derivative of an (intertwining) operator? added 217 characters in body Mar 29 comment Current Status on Langlands Program I also think that stabilization is not an issue for GL(n). Mar 29 comment Current Status on Langlands Program Mar 29 comment Current Status on Langlands Program There have been many similiar questions in the past. Mar 29 answered What is the logarithmic derivative of an (intertwining) operator? 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.