On enhanced general linear groups: nilpotent orbits and support variety for Weyl module

作者：Xue, Yunpeng^*

来源：AIMS Mathematics, 2023, 8(7): 14997-15007.

DOI：10.3934/math.2023765

• enhanced nilpotent orbits
• enhanced general linear algebric groups
• support variety
• Weyl module

Associated with a reductive algebraic group G and its rational representation (p, M) over an algebraically closed filed k, the authors define the enhanced reductive algebraic group G := G xp M, which is a product variety G x M and endowed with an enhanced cross product in [5]. If G = GL(V)xnV with the natural representation (n, V) of GL(V), it is called 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) xn 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) xn V, and obtain that it coinsides with the closure of an enhanced nilpotent orbit under some mild condition.