Supercharacters of unipotent groups defined by involutions

JOURNAL OF ALGEBRA

卷:425

Article

Andrews, Scott

关键词: Representation theory;    Groups of Lie type;    Supercharacter;    Unipotent group;   

DOI  :  10.1016/j.jalgebra.2014.11.017

来源: Elsevier

【 摘 要 】

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra groups. The resulting supercharacter theories agree with those of Andre and Neto in the case of the unipotent orthogonal and symplectic groups and generalize to a large collection of subgroups. In the unitary group case, we describe the supercharacters and superclasses in terms of labeled set partitions and calculate the supercharacter table. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free