# MathSciDoc: An Archive for Mathematician ∫

#### Representation Theorymathscidoc:1912.43211

Journal of Algebra, 485, 142-165, 2017.9
Suppose G is a reductive algebraic group, T is a Cartan subgroup of G, N= Norm (T), and W= N/T is the Weyl group. If w W has order d, it is natural to ask about the orders lifts of w to N. It is straightforward to see that the minimal order of a lift of w has order d or 2d, but it can be a subtle question which holds. We first consider the question of when W itself lifts to a subgroup of N (in which case every element of W lifts to an element of N of the same order). We then consider two natural classes of elements: regular and elliptic. In the latter case all lifts of w are conjugate, and therefore have the same order. We also consider the twisted case.
```@inproceedings{jeffrey2017lifting,
title={Lifting of elements of Weyl groups},
author={Jeffrey Adams, and Xuhua He},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112952243678771},
booktitle={Journal of Algebra},
volume={485},
pages={142-165},
year={2017},
}
```
Jeffrey Adams, and Xuhua He. Lifting of elements of Weyl groups. 2017. Vol. 485. In Journal of Algebra. pp.142-165. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112952243678771.