@article{Xue2023, 
author = {Yunpeng Xue},
title = {On enhanced general linear groups: nilpotent orbits and support variety for Weyl module},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {14997-15007},
keywords = {enhanced nilpotent orbits, enhanced general linear algebric groups, support variety, Weyl module},
url = {https://www.sciopen.com/article/10.3934/math.2023765},
doi = {10.3934/math.2023765},
abstract = {Associated with a reductive algebraic group    G and its rational representation    (  ρ  ,  M  ) over an algebraically closed filed              k      , the authors define the enhanced reductive algebraic group              G      _        :=  G      ⋉    ρ    M, which is a product variety    G  ×  M and endowed with an enhanced cross product in [5]. If              G      _        =  G  L  (  V  )      ⋉          η        V with the natural representation    (  η  ,  V  ) of        GL    (  V  ), it is called an enhanced general linear algebraic group. And the authors give a precise classification of finite nilpotent orbits via a finite set of so-called enhanced partitions of    n  =  dim  ⁡  V for the enhanced group              G      _        =      GL    (  V  )      ⋉          η        V in [6, Theorem 3.5]. We will give another way to prove this classification theorem in this paper. Then we focus on the support variety of the Weyl module for              G      _        =      GL    (  V  )      ⋉          η        V in characteristic    p, and obtain that it coinsides with the closure of an enhanced nilpotent orbit under some mild condition.}
}