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Gunter Malle

Publications and source records attributed to Gunter Malle.

81 records · Page 5Linked to original sources
arXiv2011

Simple groups admit Beauville structures

We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We also consider an analog of the result for simple algebraic groups which depends on some upper bounds for character values of regular semisimple elements in finite groups of Lie type and obtain definitive results about the variety of triples in semisimple regular classes with product 1. Finally, we prove that any finite simple group contains two conjugacy classes C,D such that any pair of elements in C x D generates the group.

math.GR↗
arXiv2010

The Largest Irreducible Representations of Simple Groups

Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non-abelian simple group can be bounded in terms of the smaller degrees. We also study the asymptotic behavior of this largest degree for finite groups of Lie type. Moreover, we show that for groups of Lie type, the Steinberg character has largest degree among all unipotent characters.

math.RT↗
arXiv2009

On the distribution of class groups of number fields

We propose a modification of the predictions of the Cohen--Lenstra heuristic for class groups of number fields in the case where roots of unity are present in the base field. As evidence for this modified formula we provide a large set of computational data which show close agreement.

math.NT↗
arXiv2009

Blocks with Equal Height Zero Degrees

We study blocks all of whose height zero ordinary characters have the same degree. We suspect that these might be the Broue-Puig nilpotent blocks.

math.GR↗
arXiv2009

Constructing representations of Hecke algebras for complex reflection groups

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras, including a generalization of the concept of $W$-graph to the situation of complex reflection groups. We then use these techniques to find models for all irreducible representations in the case of complex reflection groups of dimension at most three. Using these models we are able to verify some important conjectures on the structure of Hecke algebras.

math.RT↗
arXiv2003

Familles de caracteres de groupes de reflexions complexes

Nous etudions certains types de blocs d'algebres de Hecke associees aux groupes de reflexions complexes qui generalisent les familles de caracteres definies par Lusztig pour les groupes de Weyl. Nous determinons ces blocs pour les groupes de reflexions spetsiaux et nous etablissons un theoreme de compatibilite entre familles et d-series de Harish-Chandra. ----- We study certain types of blocks of Hecke Algebras associated to complex reflection groups which generalize the families of characters defined by Lusztig for Weyl groups. We determine these blocks for the special reflection groups and we establish a compatibility theorem between families and d-series of Harish-Chandra.

math.RT↗
arXiv2001

Counting nilpotent Galois extensions

We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends previous investigations for the case of abelian groups. In particular, the result confirms a conjecture by the second author on this function for arbitrary groups in the nilpotent case. We further prove compatibility of the conjecture with taking wreath products with the cyclic group of order 2 and give examples in degree up to 8.

math.NT↗
arXiv2001

A database for field extensions of the rationals

We report on a database of field extensions of the rationals, its properties and the methods used to compute it. At the moment the database encompasses roughly 100,000 polynomials generating distinct number fields over the rationals, of degrees up to 15. It contains polynomials for all transitive permutation groups up to that degree, and even for most of the possible combinations of signature and Galois group in that range. Moreover, whenever these are known, the fields of minimal discriminant with given group and signature have been included. The database can be downloaded from www.iwr.uni-heidelberg.de/iwr/compalg/minimum/minimum.html or from www.mathematik.uni-kassel.de~malle/minimum/minimum.html and accessed via the computer algebra system Kant. One of the aims of the compilation of this database was to test the limitations of current methods for the realization of groups as Galois groups. It turned out that these methods have limitations if the signature of the resulting Galois extension is also prescribed.

math.NT↗