Representation Theory, Quantum Groups and Piecewise-Linear Combinatorics

表示论、量子群和分段线性组合学

• 批准号: 9970533
• 负责人: Arkady Berenstein
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-05-01 至 2002-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970533&HistoricalAwards=false
• 关键词: Representation; Theory; Quantum; Groups; Piecewise

BERENSTEIN, 9970533 The proposer plans to investigate the area lying at the crossroads of representation theory of Lie groups, quantum groups and piecewise linear combinatorics. Several topics will be studied: canonical bases, crystal bases, multiplicity of modules for reductive groups and totally positive varieties. The main tools that will be used in this study are valuations on the corresponding algebras, the method of involutions, convex polyhedra and birational maps.The investigations will focus on combinatorics and various algebraic methods in trhat area. The results can be applied to study various physical symmetries and their related mathematics. This is an area that has had a large impact on physics and chemistry.

BERENSTEIN, 9970533 提议者计划研究位于李群、量子群和分段线性组合表示论十字路口的领域。将研究几个主题：规范基、晶体基、还原群模的多重性和完全正簇。本研究将使用的主要工具是相应代数的评估、对合方法、凸多面体和双有理图。研究将集中于组合数学和该领域的各种代数方法。结果可应用于研究各种物理对称性及其相关数学。 这是一个对物理和化学产生巨大影响的领域。