Representations of symmetric groups with non-trivial determinant

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:150

Article

Ayyer, Arvind¹  Prasad, Amritanshu²  Spallone, Steven³ 

[1] Indian Inst Sci, Dept Math, Bengaluru 560012, India

[2] Inst Math Sci HBNI, CIT Campus, Madras 600113, Tamil Nadu, India

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

关键词: Symmetric group;    Irreducible representations;    Permutation representations;    Determinants;    Core;    Quotients;    Core-towers;    Bell numbers;   

DOI  :  10.1016/j.jcta.2017.03.004

来源: Elsevier

【 摘 要 】

We give a closed formula for the number of partitions A of n such that the corresponding irreducible representation V-lambda of S-n has non-trivial determinant. We determine how many of these partitions are self-conjugate and how many are hooks. This is achieved by characterizing the 2-core towers of such partitions. We also obtain a formula for the number of partitions of n such that the associated permutation representation of S-n has non-trivial determinant. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free