Spinorial representations of symmetric groups

JOURNAL OF ALGEBRA

卷:544

Article

Ganguly, Jyotirmoy¹  Spallone, Steven¹ 

[1] Indian Inst Sci Educ & Res, Pune 411008, Maharashtra, India

关键词: Symmetric groups;    Representation theory;    Spinoriality;    Stiefel-Whitney class;    Spin structure;    Alternating groups;   

DOI  :  10.1016/j.jalgebra.2019.09.025

来源: Elsevier

【 摘 要 】

A real representation ( )pi of a finite group may be regarded as a homomorphism to an orthogonal group O(V). For symmetric groups S-n, alternating groups A(n), and products S-n x S-n' of symmetric groups, we give criteria for whether it lifts to the double cover Pin(V) of O(V), in terms of character values. From these criteria we compute the second Stiefel-Whitney classes of these representations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free