sheets，Jordan类和诱导轨道在exotic和enhanced模块中
Sheets, Jordan classes and induced orbits in the exotic and enhanced modules
AI总结：
本文研究了exotic和enhanced模块中的sheets和Jordan类，通过引入Jordan分层和诱导轨道理论，对adjoint表示和对称空间进行了推广，并基于Borho定理对这些模块中的sheets进行了分类。
摘要：
Kato利用几何模型为类型C的多参数 affine Hecke代数发展了exotic Deligne-Langlands对应关系，基于其exotic nilpotent cone。Achar-Henderson和Springer表明，这种exotic nilpotent与另一个似乎更简单的变种称为enhanced nilpotent cone密切相关。每个都定义为极化模块的Hilbert nullcone，即exotic Sp(2n)-module和enhanced GL(n)-module分别。在本文中，我们通过引入Jordan分层，对经典结果以及(gl(2n), sp(2n))相关的adjoint表示和对称空间进行了推广。我们开发的一个关键工具是遵循Lusztig-Spaltenstein工作的enhanced和exotic nilpotent cones中的诱导轨道理论。我们的主要应用是这些模块中sheets的分类，受Borho定理的启发。
英文摘要：
Kato developed an exotic Deligne-Langlands correspondence using a geometric model for the multiparameter affine Hecke algebra of type C, based on his exotic nilpotent cone. Achar-Henderson and Springer showed that this exotic nilpotent is intimately related to another, apparently simpler variety called the enhanced nilpotent cone. Each of these is defined as the Hilbert nullcone of a polar module, the exotic Sp(2n)-module and the enhanced GL(n)-module, respectively. In this paper we conduct a detailed study of the geometry of these two modules, by introducing the Jordan stratification, simultaneously generalising classical results on the adjoint representation as well as the symmetric space associated to (gl(2n), sp(2n)). One of the key tools we develop is the theory of induced orbits in the enhanced and exotic nilpotent cones, following the work of Lusztig-Spaltenstein. Our main application is a classification of sheets in these modules, inspired by a theorem of Borho.
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