A computational approach to the Frobenius-Schur indicators of finite exceptional groups

被引：2
|
作者：
Trefethen, Stephen [1 ]
Vinroot, C. Ryan [1 ]
机构：
[1] Coll William & Mary, Dept Math, POB 8795, Williamsburg, VA 23187 USA
来源：
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2020年 / 30卷 / 01期
基金：
欧洲研究理事会;
关键词：
Frobenius-Schur indicator; finite exceptional group; Schur index; SEMISIMPLE CONJUGACY CLASSES; REAL-VALUED CHARACTERS; CHEVALLEY-GROUPS; UNIPOTENT CHARACTERS; STEINBERG GROUPS; REDUCTIVE GROUPS; INDEXES; FIELDS;
D O I：
10.1142/S0218196719500681
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the finite exceptional groups F-4(q), E-7 (g)(ad), and Es(q) have no irreducible complex characters with Frobenius Schur indicator -1, and we list exactly which irreducible characters of these groups are not real-valued. We also give a complete list of complex irreducible characters of the Ree groups F-2(4)(q(2)) which are not real-valued, and we show the only character of this group which has Frobenius-Schur indicator -1 is the cuspidal unipotent character chi(21) found by Geck.
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页码：141 / 166
页数：26
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