Loading...
Please wait, while we are loading the content...
Similar Documents
Residues of intertwining operators for SO*6 as character identities
| Content Provider | Scilit |
|---|---|
| Author | Shahidi, Freydoon Spallone, Steven |
| Copyright Year | 2010 |
| Description | Journal: Compositio Mathematica We show that the residue at s=0 of the standard intertwining operator attached to a supercuspidal representation π⊗χ of the Levi subgroup GL_{2}$(F)×E^{1}$ of the quasisplit group SO*6(F) defined by a quadratic extension E/F of p-adic fields is proportional to the pairing of the characters of these representations considered on the graph of the norm map of Kottwitz–Shelstad. Here π is self-dual, and the norm is simply that of Hilbert’s theorem 90. The pairing can be carried over to a pairing between the character on $E^{1}$ and the character on $E^{×}$ defining the representation of $GL_{2}$(F) when the central character of the representation is quadratic, but non-trivial, through the character identities of Labesse–Langlands. If the quadratic extension defining the representation on $GL_{2}$(F) is different from E the residue is then zero. On the other hand when the central character is trivial the residue is never zero. The results agree completely with the theory of twisted endoscopy and L-functions and determines fully the reducibility of corresponding induced representations for all s. |
| Ending Page | 794 |
| Starting Page | 772 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x09004515 |
| Journal | Compositio Mathematica |
| Issue Number | 3 |
| Volume Number | 146 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2010-04-20 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics Particles and Fields Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
