Representation Theoretic Combinatorics: Constructive and Integral

表示理论组合学：构造性和积分

• 批准号: 0070609
• 负责人: Robert Liebler
• 金额: $ 7.8万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070609&HistoricalAwards=false
• 关键词: Representation; Theoretic; Combinatorics; Constructive; Integral

Non Abelian difference sets, Williamson-like Hadamard Matrices, integral Hecke algebras of diagram geometries and cyclotomic association schemes will be studied using and developing a representation theory of finitely based algebras over number rings. Typical problems include explicit constructions for small parameter cases that are now open, computation of the arithmetic invariants (Smith normal form) of classical incidence maps, and enumeration of fusion schemes within a classical Hecke algebra.By moving from fields to number rings this work builds a broader bridge between pure mathematics (number theory, abstract algebra) and combinatorial constructions (finite geometry, algebraic combinatorics). This work will lead to more penetrating mathematical tools to study known combinatorial objects and the possibility to better design and build combinatorial objects to meet specific "spectral" specifications. These kinds of ombinatorial constructions have had great value in cryptography and digital communication system design (e.g. high speed modems and digital cellular telephony). This grant also supports guest speakers at a long running regional Algebraic Combinatorics Seminar that includes and benefits faculty from The University of Wyoming, The University of Colorado at Denver and Colorado State University (http://www.math.cudenver.edu/~wcherowi/algcomb.html)

非阿贝尔差集，Williamson-like Hadamard矩阵，图几何的积分Hecke代数和分圆结合方案将使用和发展数环上基于代数的表示理论进行研究。 典型的问题包括明确的小参数的情况下，现在开放的建设，计算的算术不变量（史密斯范式）的经典关联映射，并枚举融合计划内的一个经典Hecke algebrafic.By领域移动到数环这项工作建立了一个更广泛的桥梁之间的纯数学（数论，抽象代数）和组合结构（有限几何，代数组合）。 这项工作将导致更深入的数学工具来研究已知的组合对象和可能性，以更好地设计和构建组合对象，以满足特定的“光谱”规格。 这类组合结构在密码学和数字通信系统设计（例如高速调制解调器和数字蜂窝电话）中具有很大的价值。 该补助金还支持长期运行的区域代数组合学研讨会的客座演讲者，该研讨会包括并使教师受益于 怀俄明州大学、丹佛的科罗拉多大学和科罗拉多州立大学（http：//www.math.cudenver.edu/crowcherowi/algcomb.html）