Guralnick, Robert M.; Pham Huu Tiep Low-dimensional representations of special linear groups in cross characteristics. (English) Zbl 0974.20014 Proc. Lond. Math. Soc., III. Ser. 78, No. 1, 116-138 (1999). The low-dimensional projective irreducible representations in cross characteristics of the projective special linear group \(\text{PSL}_n(q)\) are investigated. If \(n\geq 3\) and \((n,q)\neq(3,2)\), \((3,4)\), \((4,2)\), \((4,3)\), all such representations of the first degree (which is \((q^n-q)/(q-1)-\kappa\) with \(\kappa=0\) or \(1\)) and the second degree (which is \((q^n-1)/(q-1)\)) come from Weil representations. We show that the gap between the second and the third degree is roughly \(q^{2n-4}\). Reviewer: Pham Huu Tiep (Columbus) Cited in 19 Documents MSC: 20C33 Representations of finite groups of Lie type 20G05 Representation theory for linear algebraic groups 20C20 Modular representations and characters 20G40 Linear algebraic groups over finite fields Keywords:projective special linear groups; low-dimensional representations in cross characteristics; Weil representations PDFBibTeX XMLCite \textit{R. M. Guralnick} and \textit{Pham Huu Tiep}, Proc. Lond. Math. Soc. (3) 78, No. 1, 1 (1999; Zbl 0974.20014) Full Text: DOI