Representation Degrees, Character Values and Applications

表征程度、特征值及应用

• 批准号: EP/H018891/1
• 负责人: Martin Liebeck
• 金额: $ 6.17万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH018891%2F1
• 关键词: Representation; Degrees; Character; Values; Applications

In recent years there has been a growing use of Representation Theory in Asymptotic Group Theory and related topics.On the one hand, there is the rather new subject of representation growth, somewhat analogous to the classical study ofsubgroup growth. On the other hand, the solutions of various seemingly unrelated problems - such as random walks on groups,or random generation of simple groups, or word maps on groups - require new results in representation theory, involving character degreesand values. In this proposal we plan to study several quantitative aspects of representation theory, and to applythem in a wide variety of such contexts.

近年来，表示论在渐近群论及相关课题中的应用越来越广泛。一方面，表示增长是一个相当新的课题，有点类似于子群增长的经典研究。另一方面，各种看似无关的问题的解决方案-如群上的随机游动，或简单群的随机生成，或群上的词映射-需要表示论的新结果，涉及特征标度和值。在这个建议中，我们计划研究表征理论的几个定量方面，并将其应用于各种各样的此类背景。

项目成果

On fixed points of elements in primitive permutation groups

关于本原置换群中元素的不动点

• DOI: 10.1016/j.jalgebra.2014.08.038
• 发表时间: 2015
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Liebeck M

Character bounds for finite groups of Lie type

Lie 类型有限群的字符界限

• DOI: 10.4310/acta.2018.v221.n1.a1
• 发表时间: 2018
• 期刊: Acta Mathematica
• 影响因子: 3.7
• 作者: Bezrukavnikov R

The density of representation degrees

代表性程度的密度

• DOI: 10.4171/jems/339
• 发表时间: 2012
• 期刊: Journal of the European Mathematical Society
• 影响因子: 2.6
• 作者: Liebeck M

Fixed points of elements of linear groups

线性群元素的不动点

• DOI: 10.1112/blms/bdr025
• 发表时间: 2011
• 期刊: Bulletin of the London Mathematical Society
• 影响因子: 0.9
• 作者: Liebeck M

Character ratios, representation varieties and random generation of finite groups of Lie type

Lie型有限群的字符比、表示多样性和随机生成

• DOI: 10.1016/j.aim.2020.107386
• 发表时间: 2020
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Liebeck M