# Linear representation theory of projective special linear group of degree two over a finite field

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## Contents |

This article gives specific information, namely, linear representation theory, about a family of groups, namely: projective special linear group of degree two.

View linear representation theory of group families | View other specific information about projective special linear group of degree two

This article describes the linear representation theory of the projective special linear group of degree two over a finite field. The order (size) of the field is , and the characteristic prime is . is a power of . We denote the group as or .

See also the linear representation theories of: general linear group of degree two, projective general linear group of degree two, and special linear group of degree two.

## Summary

Item | Value |
---|---|

degrees of irreducible representations over a splitting field (such as or ) | Case congruent to 1 mod 4 (e.g., ): 1 (1 time), (2 times), ( times), (1 time), ( times) Case congruent to 3 mod 4 (e.g., ): 1 (1 time), (2 times), ( times), (1 time), ( times) Case even (e.g., ): 1 (1 time), ( times), (1 time), ( times) |

number of irreducible representations | Case odd: ; Case even: . See number of irreducible representations equals number of conjugacy classes, element structure of projective special linear group of degree two over a finite field#Conjugacy class structure |

quasirandom degree (minimum possible degree of nontrivial irreducible representation) | Case congruent to 1 mod 4 (e.g., ): Case congruent to 3 mod 4 (e.g., ): Case even: |

maximum degree of irreducible representation over a splitting field | |

lcm of degrees of irreducible representations over a splitting field | Case odd: , Case even: |

sum of squares of degrees of irreducible representations over a splitting field | Case odd: , case even: equal to the group order. See sum of squares of degrees of irreducible representations equals group order |