Gösterimlerin Endoskopik Sınıflandırılması

Özet (abstract)

We shall outline a classification [A] of the automorphic representations of special orthogonal and symplectic groups in terms of those of general linear groups. This necessarily includes a classification of local L-packets of representations. It also requires a classification of the extended packets that are the local constituents of nontempered automorphic representations. Our description will be brief. In particular, we will restrict it to quasisplit ∗ orthogonal and symplectic groups G, even though at least some of the results can be extended (not without effort) to inner twists of G. The methods rest ultimately on two comparisons of trace formulas. One is the spectral identity that is the end product of the stabilization of the trace formula for G. This was established some years ago [A1], under the assumption of the fundamental lemma. It now holds without condition, thanks to the work of Waldspurger [W1][W2], the recent breakthrough by Ngo [N], and the extensions of Chaudouard and Laumon [CL1] [CL2]. The other is the spectral identity given by the stabilization of the twisted trace formula for GL(N). This formula is still conditional. The relevant twisted fundamental lemmas are now known [W3], [W4], at least up to the twisted variants of [CL1] and [CL2]. The problem is to develop twisted generalizations of the techniques of [A1] and related papers. Until this is done, the results we describe here have also to be regarded as conditional. We take F to be a local or global field of characteristic 0, and G to be a quasisplit, special orthogonal or symplectic group over F. Then G has a complex dual group G, and a corresponding

Yazarların özeti; kaynağından alınmıştır. Colloquium Publications - American Mathematical Society/Colloquium Publications, 2013 · DOI ↗