Supercharacters of discrete algebra groups

Combinatorial Hopf algebra of supercharacters of type D

We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type D over a finite field. Also, we make further comments with respect to types B and C. Type A was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types. Résumé. Nous c...

Supercharacters of Unipotent Groups Defined by Involutions (extended Abstract)

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 André and Neto in the case of the unipotent orthogonal and symplectic matrices ...

Structural Properties of Inner Amenable Discrete Groups

Supercharacters and Hopf Monoids

Before the workshop, we suggested that the following reading list [1, 2, 3, 4, 5, 6] would be a good refreshment for all of us. At the start of the workshop, we identified the following problems that were worth considering given the recent progress in the area. 1. Higman’s conjecture. 2. Compute the antipode of the monoid scf(U) in the supercharacter basis. 3. Explicitly describe the multiplica...

Algebra and discrete mathematics

In this work first we study the properties of nearsemirings to introduce an α-radical. Then we observe the role of near-semirings in generalized linear sequential machines, and we test the minimality through the radical.