Generalizations of Schur functions

Schur 函数的推广

• 批准号: RGPIN-2015-03915
• 负责人: vanWilligenburg, Stephanie
• 金额: $ 1.46万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589466
• 关键词: Generalizations; Schur; functions

Schur functions were first studied by Cauchy in 1815, although they were named after Schur, who in 1901 showed that they were isomorphic to an irreducible character of a symmetric group under the Frobenius character map. Since then they have arisen in a variety of areas including algebraic geometry where Schur functions agree with Schubert classes in the cohomology ring of the complex Grassmannian, and quantum mechanics where they are related to quantum states.

舒尔函数最早是由柯西在1815年研究的，尽管它们是以舒尔的名字命名的，舒尔在1901年证明了它们同构于Frobenius字符映射下对称群的一个不可约字符。从那时起，它们出现在各种领域，包括代数几何，其中舒尔函数在复格拉斯曼的上同环中与舒伯特类一致，以及量子力学，其中它们与量子态相关。