经典群不变理论的胞腔第二基本定理
表示论
2018-01-12 v4
摘要
我们证明了作用在张量空间上的辛群和正交群的中心化代数是整数上的胞腔代数。我们通过提供研究图表代数塔的商塔的公理框架来实现这一点。我们的框架也涵盖了作用在混合张量空间上的一般线性群的中心化代数。我们还给出了从代数的图表版本到张量空间上中心化代数的同态核的描述，这些构成了不变理论第二基本定理的版本。
引用
@article{arxiv.1610.09009,
title = {The cellular second fundamental theorem of invariant theory for classical groups},
author = {Christopher Bowman and John Enyang and Frederick Goodman},
journal= {arXiv preprint arXiv:1610.09009},
year = {2018}
}
备注
To appear in International Mathematics Research Notices. This arXiv version includes several appendices which will not be included in the published version, in particular material on Murphy type cellular bases of the walled Brauer algebras, and of the quotients of these algebras acting on mixed tensor space