תקציר
We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation π = I(1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This computation is independent of the theory of the symmetric square lifting of [IV] of automorphic and admissible representations of SL(2) to PGL(3). It leads - see [FK] - to a proof of the (unstable) fundamental lemma in the theory of the symmetric square lifting, namely that corresponding spherical functions (on PGL(2) and PGL(3)) are matching: they have matching orbital integrals. The new case in [FK] is the unstable one. A direct local proof of the fundamental lemma is given in [V].
שפה מקורית | אנגלית |
---|---|
עמודים (מ-עד) | 307-315 |
מספר עמודים | 9 |
כתב עת | Israel Journal of Mathematics |
כרך | 134 |
מזהי עצם דיגיטלי (DOIs) | |
סטטוס פרסום | פורסם - 2003 |
פורסם באופן חיצוני | כן |