Generalizations of Schur functions

柯西在1815年首先研究了舒尔函数，尽管它们是以舒尔命名的，他在1901年证明了它们同构于一个对称群在Frobenius特征标映射下的不可约特征标。从那时起，他们已经出现在各种领域，包括代数几何的舒尔职能同意舒伯特类的上同调环的复杂格拉斯曼，和量子力学，他们有关的量子态。

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.