The maximal discrete extension of the Hermitian modular group
Journal article, 2021

Let Gamma(n)(O-K) denote the Hermitian modular group of degree n over an imaginary-quadratic number field K. In this paper we determine its maximal discrete extension in SU(n, n; C), which co-incides with the normalizer of Gamma(n)(O-K). The description involves the n-torsion subgroup of the ideal class group of K. This group is defined (K) over cap (n) and we can describe the ramified over a particular number field primes in it. In the case n = 2 we give an explicit description, which involves generalized Atkin-Lehner involutions. Moreover we find a natural characterization of this group in SO(2, 4).

maximal discrete extension

Hermitian modular group

normalizer

Atkin-Lehner involution

orthogonal group

Author

Aloys Krieg

RWTH Aachen University

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Annalena Wernz

RWTH Aachen University

Documenta Mathematica

1431-0635 (ISSN) 1431-0643 (eISSN)

Vol. 26 1871-1888

Subject Categories

Discrete Mathematics

DOI

10.25537/dm.2021v26.1871-1888

More information

Latest update

7/6/2022 2