Loading...
Please wait, while we are loading the content...
Similar Documents
Residues of Intertwining Operators for SO ∗ 6 as Character Identities
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shahidi, Freydoon Spallone, Steven |
| Copyright Year | 2009 |
| Abstract | We show that the residue at s = 0 of the standard intertwining operator attached to a supercuspidal representation π ⊗ χ of the Levi subgroup GL2(F ) × E1 of the quasisplit group SO6(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 E1 and the character of E× defining the representation of GL2(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 GL2(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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.ou.edu/~sspallone/Papers/CharIds.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Dual Graph - visual representation Personality Character Sense of identity (observable entity) Subgroup A Nepoviruses Twisted |
| Content Type | Text |
| Resource Type | Article |
