TY - JOUR
T1 - Low-dimensional representations of special linear groups in cross characteristics
AU - Guralnick, Robert M.
AU - Tiep, Pham Huu
N1 - Funding Information:
The work of the first author was partially supported by the NSF. 1991 Mathematics Subject Classification: 20C20, 20C33.
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
SN - 0024-6115
VL - 78
SP - 116
EP - 138
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 1
ER -