On a converse theorem for G2 over finite fields

被引：0

作者：

Liu, Baiying ^{[1
]}

Zhang, Qing ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47906 USA

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak Ro, Daejeon 34141, South Korea

来源：

MATHEMATISCHE ANNALEN | 2022年 / 383卷 / 3-4期

关键词：

FOURIER-JACOBI MODELS; REDUCTIVE GROUPS; GAMMA FACTORS; UNIPOTENT SUPPORT; REPRESENTATIONS; CONJECTURE; UNIQUENESS; GL(N);

D O I：

10.1007/s00208-021-02250-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split G(2) over finite fields k of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, GL(1) and GL(2)-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of G(2)(k).

引用

页码：1217 / 1283

页数：67

共 50 条

[21] The Minimal Ramification Problem for Rational Function Fields over Finite Fields
Bary-Soroker, Lior
Entin, Alexei
Fehm, Arno
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (21) : 18199 - 18253
[22] On the asymptotic Fermat's last theorem over number fields
Sengun, Mehmet Haluk
Siksek, Samir
COMMENTARII MATHEMATICI HELVETICI, 2018, 93 (02) : 359 - 375
[23] ON TODA SYSTEM WITH CARTAN MATRIX G2
Ao, Weiwei
Lin, Chang-Shou
Wei, Juncheng
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (08) : 3525 - 3536
[24] Gamma factors and quadratic extension over finite fields
Nien, Chufeng
MANUSCRIPTA MATHEMATICA, 2019, 158 (1-2) : 31 - 54
[25] On Gabor orthonormal bases over finite prime fields
Iosevich, Alex
Kolountzakis, Mihalis
Lyubarskii, Yurii
Mayeli, Azita
Pakianathan, Jonathan
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2021, 53 (02) : 380 - 391
[26] Arithmetic properties of polynomial specializations over finite fields
Pollack, Paul
ACTA ARITHMETICA, 2009, 136 (01) : 57 - 79
[27] On a relative version of a theorem of Bogomolov over perfect fields and its applications
Dao Phuong Bac
Nguyen Quoc Thang
JOURNAL OF ALGEBRA, 2010, 324 (06) : 1259 - 1278
[28] Extended T-System of Type G2
Li, Jian-Rong
Mukhin, Evgeny
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2013, 9
[29] Permutation polynomials over finite fields - A survey of recent advances
Hou, Xiang-dong
FINITE FIELDS AND THEIR APPLICATIONS, 2015, 32 : 82 - 119
[30] ON THE NUMBER OF POINTS OF NILPOTENT QUIVER VARIETIES OVER FINITE FIELDS
Bozec, Tristan
Schiffmann, Olivier
Vasserot, Eric
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2020, 53 (06): : 1501 - 1544

← 1 2 3 4 5 →