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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635388
• 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.

库奇（Cauchy）在1815年首先研究了Schur功能，尽管它们是以Schur的名字命名的，后者在1901年表明它们与Frobenius角色图下的对称群体的不可还原性具有同构。从那时起，它们就在各个领域都出现，包括代数几何形状，Schur函数与复杂的Grassmannian的辅助阶层和与量子状态相关的量子力学中的Schubert类别一致。