| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Normalized intertwining operators and nilpotent elements in the Langlands dual group | Alexander Braverman
; David Kazhdan
; | Date: |
11 Jun 2002 | Subject: | Representation Theory; Algebraic Geometry; Number Theory | math.RT math.AG math.NT | Abstract: | Let $F$ be a local non-archimedian field and let $G$ be a group of points of a split reductive group over $F$. For a parabolic subgroup $P$ of $G$ we set $X_P=G/[P,P]$. For any two parabolics $P$ and $Q$ with the same Levi component $M$ we construct an explicit unitary isomorphism $L^2(X_P) o L^2(X_Q)$ (which depends on a choice of an additive character of $F$). The formula for the above isomorphism involves the action of the principal nilpotent element in the Langlands dual group of $M$ on the unipotent radicals of the corresponding dual parabolics. We use the above isomorphisms to define a new space $calS(G,M)$ of functions on $X_P$ (which depends only on $P$ and not on $M$). We explain how this space may be applied in order to reformulate in a slightly more elegant way the construction of $L$-functions associated with the standard representation of a classical group due to Gelbart, Piatetski-Shapiro and Rallis. | Source: | arXiv, math.RT/0206119 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |