The average size of the kernel of a matrix and orbits of linear groups, II: duality

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Rossmann, Tobias¹ 

[1] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

关键词: Average size of a kernel;    Duality;    Conjugacy classes;    p-Groups;    Lie rings;    Unipotent groups;   

DOI  :  10.1016/j.jpaa.2019.106203

来源: Elsevier

【 摘 要 】

Define a module representation to be a linear parameterisation of a collection of module homomorphisms over a ring. Generalising work of Knuth, we define duality functors indexed by the elements of the symmetric group of degree three between categories of module representations. We show that these functors have tame effects on average sizes of kernels. This provides a general framework for and a generalisation of duality phenomena previously observed in work of O'Brien and Voll and in the predecessor of the present article. We discuss applications to class numbers and conjugacy class zeta functions of p-groups and unipotent group schemes, respectively. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free