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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 42 NO.6 / (1990))
On Twisted Orbital Integral Identities for $PGL(3)$ over a $p$-Adic Field
David Joyner,
Pages. 1098-1130
Abstract The object of this paper is to prove certain $p$-adic orbital integral identities needed in order to accomplish the symmetric square transfer via the twisted Arthur trace formula. Only $S$5 of this article contains original material, the rest of it is due to R. Langlands. Very briefly, we reduce the problem of proving certain orbital integral identities for ""matching"" functions in the respective Hecke algebras to two counting problems on the buildings. We give Langlands' solutions of one of these problems on the buildings. We give Langlands' solution of one of these problems in the case of the unit elements of the respective hecke algebras and $S$5 provides the solution to the other one, again, in the unit element case. The main results assume $p
eq 2$.
Contents 0. Contents 1. Introduction 1.1 History 1.2 $L$-parameters and the transfer from $SL(2)$ to $PGL(3)$. 1.3 The Jacquet-Shalika norm maps 1.4 The fundamental lemmas 2. The identities in the split case 2.1 Summary 2.2 Background on twisted integration formulas 2.3 The Satake transform on $PGL(3),\; SL(2),\; PGL(2)$ 2.4 The fundamental identities in the split case 3. The reduction in the non-split case to buildings 3.1 Summary 3.2 The reduction 4. The Buildings for $PGL(3)$ and $SL(2)$ 5. The Buildings for $PGL(3),\; PGL(3),\; PGL(2)$
Key words
Mathmatical Subject Classification 11F70,11R39,22E50