Low-dimensional representations of special linear groups in cross characteristics

Robert M. Guralnick, Pham Huu Tiep

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49 Scopus citations

Abstract

The low-dimensional projective irreducible representations in cross characteristics of the projective special linear group Ln (q) are investigated. If n ≥ 3 and (n,q) ≠ (3,2), (3,4), (4,2), (4,3), all such representations of the first degree (which is (qn - q)/(q - 1) - κn with κn = 0 or 1) and the second degree (which is (qn - 1)/(q - 1)) come from Weil representations. We show that the gap between the second and the third degree is roughly q2n-4.

Original languageEnglish (US)
Pages (from-to)116-138
Number of pages23
JournalProceedings of the London Mathematical Society
Volume78
Issue number1
DOIs
StatePublished - Jan 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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