### Abstract

Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we determine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r, r a prime divisor of the group order.

Original language | English (US) |
---|---|

Pages (from-to) | 2093-2167 |

Number of pages | 75 |

Journal | Communications in Algebra |

Volume | 24 |

Issue number | 6 |

State | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*24*(6), 2093-2167.

**Minimal characters of the finite classical groups.** / Tiep, Pham Huu; Zalesskii, Alexander E.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 24, no. 6, pp. 2093-2167.

}

TY - JOUR

T1 - Minimal characters of the finite classical groups

AU - Tiep, Pham Huu

AU - Zalesskii, Alexander E.

PY - 1996

Y1 - 1996

N2 - Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we determine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r, r a prime divisor of the group order.

AB - Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we determine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r, r a prime divisor of the group order.

UR - http://www.scopus.com/inward/record.url?scp=0010763967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010763967&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0010763967

VL - 24

SP - 2093

EP - 2167

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 6

ER -