TY - JOUR

T1 - Low-dimensional representations of special linear groups in cross characteristics

AU - Guralnick, Robert M.

AU - Tiep, Pham Huu

PY - 1999/1

Y1 - 1999/1

N2 - 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.

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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U2 - 10.1112/S0024611599001720

DO - 10.1112/S0024611599001720

M3 - Article

AN - SCOPUS:0001292623

VL - 78

SP - 116

EP - 138

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 1

ER -