L. Di Martino | Searcharxiv

arXiv2016

Almost cyclic elements in Weil representations of finite classical groups

This paper is a significant part of a general project aimed to classify all irreducible representations of finite quasi-simple groups over an algebraically closed field, in which the image of at least one element is represented by an almost cyclic matrix. (A square matrix $M$ is called almost cyclic if it is similar to a block-diagonal matrix with two blocks, such that one block is scalar and another block is a matrix whose minimum and characteristic polynomials coincide. Reflections and transvections are examples of almost cyclic matrices. The paper focuses on the Weil representations of finite classical groups, as there is strong evidence that these representations play a key role in the general picture.

math.GR↗

arXiv2012

On generators and representations of the sporadic simple groups

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable a in F, M is similar to diag(a Id_h, M_1), where M_1 is cyclic and 0 <= h <= n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.

math.RT↗