Normalized intertwining operators and nilpotent elements in the Langlands dual group
| dc.creator | Braverman, Alexander | |
| dc.creator | Kazhdan, David | |
| dc.date | 2002-06-11 | |
| dc.date | 2002-06-21 | |
| dc.date.accessioned | 2026-07-07T04:49:04Z | |
| dc.date.available | 2026-07-07T04:49:04Z | |
| dc.description | 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 $L^2(X_P)\to L^2(X_Q)$ (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. | |
| dc.description | 22 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0206119 | |
| dc.identifier | http://arxiv.org/abs/math/0206119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64285 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Normalized intertwining operators and nilpotent elements in the Langlands dual group | |
| dc.type | text |