This article is to contribute to the classification of finite-dimensional complex pointed Hopf algebras with Weyl groups of E8. Many papers are about the classification of finite dimensional pointed Hopf algebras, for example, [AS98, AS02, AS00, AS05, He06, AHS08, AG03, AFZ, AZ07, Gr00, Fa07, AF06, AF07, ZZC, ZC]. In these research ones need the centralizers and character tables of groups. In t...

Abstract We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated one degree. Each these homogeneous is one-dimensional can be cohomologically constructed via a BGG resolution involving every (infinite dimensional) standard representation category. hence determine complete first row inverse parabolic p -Kazhdan–Lusztig...

Using recent absolute irreducibility testing algorithms, we derive new irreducibility forms. These are integer polynomials in variables which are the generic coefficients of a multivariate polynomial of a given degree. A (multivariate) polynomial over a specific field is said to be absolutely irreducible if it is irreducible over the algebraic closure of its coefficient field. A specific polyno...

We have started this class by studying the representation theory of the symmetric group Sn over the complex numbers. We finish by giving a brief introduction to the representation theory of Sn over a field F of positive characteristic p. We will also establish a connection between the representations of ŝlp and those of FSn. This connection was one of motivations to consider Kac-Moody algebra a...