https://hal.inria.fr/hal-01207592Andrews, ScottScottAndrewsUniversity of Colorado [Boulder]Supercharacters of Unipotent GroupsHAL CCSD2014supercharacterrepresentation theoryunipotent grouplabeled set partition[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Episciences Iam, CoordinationLouis J. Billera and Isabella Novik2015-10-01 09:28:582019-07-26 13:44:052015-10-01 09:32:39enConference papershttps://hal.inria.fr/hal-01207592/document10.46298/dmtcs.2383application/pdf1\textbfAbstract. 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 AndrĂ© and Neto in the case of the unipotent orthogonal and symplectic matrices 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. \bigbreak