Abstract
Let G be a finite group. The ring RK(G) of virtual characters of G over the field K is a λ-ring; as such, it is equipped with the so-called Γ-filtration, first defined by Grothendieck. We explore the properties of the associated graded ring RK⁎(G), and present a set of tools to compute it through detailed examples. In particular, we use the functoriality of RK⁎(−), and the topological properties of the Γ-filtration, to explicitly determine the graded character ring over the complex numbers of every group of order at most 8, as well as that of dihedral groups of order 2p for p prime.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
