Coxeter groups and related structures

考克塞特群及相关结构

• 批准号: 355458-2013
• 负责人: Hohlweg, Christophe
• 金额: $ 1.38万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=527768
• 关键词: Coxeter; groups; related; structures

My primary area of research is algebraic combinatorics. It is a highly active area of mathematics, with many connections to algebraic geometry, convex geometry, representation theory, topology, mathematical physics and statistical mechanics, among many others. I am more precisely interested on the combinatorial and geometrical aspects of the study of Coxeter (mirror reflection) groups and their related structures. Coxeter groups appear in very many domains of mathematics, for instance, as symmetry groups of regular polytopes, as Weyl groups of semi-simple Lie algebras and Kac-Moody algebras, and as triangle groups in geometry (Euclidean and hyperbolic). Properties of these groups are often key to the understanding of related structures.

我的主要研究领域是代数组合学。它是数学高度活跃的领域，与代数几何形状，凸几何，表示理论，拓扑，数学物理学和统计力学等有许多联系。我对Coxeter研究（镜像）组及其相关结构的研究的组合和几何方面更加精确感兴趣。 Coxeter组出现在数学的许多领域中，例如，作为常规多型的对称组，如半简单的lie代数和KAC-MOODY代数，以及几何形状（欧几里得和双胞胎）中的三角形基团。这些组的特性通常是对相关结构的理解的关键。