有限域上辛形式对称空间的特征映射
表示论
2021-02-15 v2 组合数学
摘要
对称群的特征映射是一个将对称群的表示论与对称函数相关联的同构。针对有限域上辛形式的对称空间构造了一个类似的同构，其中球函数被映为带参数 的 Macdonald 多项式。抛物诱导的类似物被解释为对称函数的某种乘法。给出了其在带参数 的斜 Macdonald 多项式的 Schur-正性以及球函数值的组合公式方面的应用。
引用
@article{arxiv.1906.05966,
title = {A characteristic map for the symmetric space of symplectic forms over a finite field},
author = {Jimmy He},
journal= {arXiv preprint arXiv:1906.05966},
year = {2021}
}
备注
Major revision. v1 Theorem 4.7 is incorrect and replaced with v2 Theorem 4.9. The product defined in Section 4.4 is replaced with a module structure. The application to the structure constants for Macdonald polynomials is replaced with an application to the Schur expansion of skew Macdonald Polynomials. The dependence on character sheaves is removed and the connection explained in a new section