### 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 (q^{n} - q)/(q - 1) - κ_{n} with κ_{n} = 0 or 1) and the second degree (which is (q^{n} - 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) |
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Pages (from-to) | 116-138 |

Number of pages | 23 |

Journal | Proceedings of the London Mathematical Society |

Volume | 78 |

Issue number | 1 |

State | Published - Jan 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*78*(1), 116-138.

**Low-dimensional representations of special linear groups in cross characteristics.** / Guralnick, Robert M.; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 78, no. 1, pp. 116-138.

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0001292623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001292623&partnerID=8YFLogxK

M3 - Article

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 -