Low-dimensional representations of special linear groups in cross characteristics

Robert M. Guralnick; Pham Huu Tiep

doi:10.1112/S0024611599001720

Low-dimensional representations of special linear groups in cross characteristics

Robert M. Guralnick, Pham Huu Tiep

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44 Scopus citations

Abstract

The low-dimensional projective irreducible representations in cross characteristics of the projective special linear group L_n (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) - κ_n with κ_n = 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 q^2n-4.

Original language	English (US)
Pages (from-to)	116-138
Number of pages	23
Journal	Proceedings of the London Mathematical Society
Volume	78
Issue number	1
DOIs	https://doi.org/10.1112/S0024611599001720
State	Published - Jan 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1112/S0024611599001720

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AB - 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.

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