## Abstract

Let o be a complete discrete valuation ring with finite residue field k of odd characteristic. Let G be a general or special linear group or a unitary group defined over o and let g denote its Lie algebra. For every positive integer ℓ, let K^{ℓ} be the ℓ-th principal congruence subgroup of G(o). A continuous irreducible representation of G(o) is called regular of level ℓ if it is trivial on K^{ℓ+1} and its restriction to K^{ℓ}/K^{ℓ+1}≃g(k) consists of characters with G(k‾)-stabiliser of minimal dimension. In this paper we construct the regular characters of G(o), compute their degrees and show that the latter satisfy Ennola duality. We give explicit uniform formulae for the regular part of the representation zeta functions of these groups.

Original language | English |
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Pages (from-to) | 116-137 |

Number of pages | 22 |

Journal | Journal of Algebra |

Volume | 496 |

DOIs | |

State | Published - 15 Feb 2018 |

Externally published | Yes |

## Keywords

- Ennola duality
- Representation zeta functions
- Representations of compact p-adic groups

## ASJC Scopus subject areas

- Algebra and Number Theory

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