Abstract
Abstract This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is represented by an almost cyclic matrix (that is, a square matrix M of size n over a field 𝔽 {\mathbb{F}} with the property that there exists α ∈ 𝔽 {\alpha\in\mathbb{F}} such that M is similar to diag ( α ⋅ Id k , M 1 ) {\operatorname{diag}(\alpha\cdot\mathrm{Id}_{k},M_{1})} , where M 1 {M_{1}} is cyclic and 0 ≤ k ≤ n {0\leq k\leq n} ). While a previous paper dealt with the Weil representations of finite classical groups, which play a key role in the general picture, the present paper provides a conclusive answer for all cross-characteristic projective irreducible representations of the finite quasi-simple groups of Lie type and their automorphism groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.