Low-Dimensional Representations of Special Linear Groups in Cross Characteristics |
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| Authors: | Guralnick Robert M; Tiep Pham Huu |
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| Institution: | Department of Mathematics, University of Southern California Los Angeles, CA 90089-1113, U.S.A. E-mail: guralnic{at}math.usc.edu
Department of Mathematics, University of Florida Gainesville, FL 32611-8105, U.S.A. E-mail: tiep{at}math.ufl.edu |
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| Abstract: | The low-dimensional projective irreducible representations incross characteristics of the projective special linear groupPSLn(q) are investigated. If n  3 and (n, q)  (3,2), (3,4), (4,2), (4,3), all such representationsof the first degree (which is (qn – q)/(q – 1) – with = 0 or 1) and the second degree (which is (qn –1)/(q – 1) come from Weil representations. We show thatthe gap between the second and the third degree is roughly q2n-4.1991 Mathematics Subject Classification: 20C20, 20C33. |
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