A LOCAL LANGLANDS PARAMETERIZATION FOR GENERIC SUPERCUSPIDAL REPRESENTATIONS OF p-ADIC G2

被引：2

作者：

Harris, Michael ^{[1
]}

Khare, Chandrashekhar B. ^{[2
]}

Thorne, Jack A. ^{[3
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] UCLA, Dept Math, Los Angeles, CA USA

[3] Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge, England

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2023年 / 56卷 / 01期

基金：

美国国家科学基金会; 欧洲研究理事会; 欧盟地平线“2020”;

关键词：

GALOIS GROUP; G(2); FUNCTORIALITY; CONJECTURE; THEOREMS; MODULES;

D O I：

10.24033/asens.2533

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

- We construct a Langlands parameterization of supercuspidal representations of G2 over a p-adic field. More precisely, for any finite extension K/Qp we will construct a bijection .Cg :A & DEG;g(G2, K)-> g & DEG;(G2, K) from the set of generic supercuspidal representations of G2(K) to the set of irreducible continuous homomorphisms p : WK > G2(C) with WK the Weil group of K. The construction of the map is simply a matter of assembling arguments that are already in the literature, together with a previously unpublished theorem of G. Savin on exceptional theta correspondences, included as an appendix. The proof that the map is a bijection is arithmetic in nature, and specifically uses automorphy lifting theorems. These can be applied thanks to a recent result of Hundley and Liu on automorphic descent from GL(7) to G2.

引用

页码：257 / 286

页数：32

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