Pyramids and decomposition numbers for the symmetric and general linear groups

对称和一般线性群的金字塔和分解数

• 批准号: DP0986349
• 负责人: Prof Andrew Mathas
• 金额: $ 32.9万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2009
• 资助国家: 澳大利亚
• 起止时间: 2009-01-29 至 2016-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0986349
• 关键词: Pyramids; decomposition; numbers; symmetric; general

This project takes a novel approach to the decomposition number problem for the symmetric and general linear groups by setting up a new framework for computing them using the combinatorics of pyramids. The decomposition numbers of an algebra are an important statistic which gives detailed structural information about its representations. These numbers can be used to compute the dimensions of the irreducible representations of the algebra and they play an important role in the applications of representation theory to other fields such as knot theory and statistical mechanics.

这个项目为对称和一般线性群的分解数问题提供了一种新的方法，通过建立一个新的框架来使用金字塔的组合学来计算它们。代数的分解数是一个重要的统计量，它给出了关于其表示的详细的结构信息。这些数字可以用来计算代数的不可约表示的维度，它们在表示理论在其他领域的应用中起着重要的作用，如纽结理论和统计力学。