Frank Lübeck   

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Preprints

From this page you can download preprint versions of some articles.

CHEVIE

Lübeck, F., Charaktertafeln für die Gruppen CSp6(q) mit ungeradem q und Sp6(q) mit geradem q, Dissertation, Universität Heidelberg (1993)
(formatted for the IWR-Preprint 93-61)

[BibTeX-Entry] [pdf-file]

In this application of Deligne-Lusztig theory the complete generic character tables of the groups mentioned in the title were computed. This is used to show that certain symplectic groups occur as Galois groups over the rational number field.

Geck, M. and Hiss, G. and Lübeck, F. and Malle, G. and Pfeiffer, G., CHEVIE - A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras, Appl. Algebra Engrg. Comm. Comput., 7, (1996), p. 175--210

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

An overview of the CHEVIE-system. This should be used as reference when you use CHEVIE for your work. The description of the part implemented in GAP is a bit outdated.

Reeder, M. (and an appendix by Lübeck, F.), Formal degrees and L-packets of unipotent discrete series representations of exceptional p-adic groups, J. Reine Angew. Math., 520, (2000), p. 37--93

An application of CHEVIE to p-adic groups. Ask here for a preprint of the main paper. The appendix is here:

[BibTeX-Entry] [dvi-file (with hyperlinks)] [postscript-file] [pdf-file]

Brauer trees in exceptional groups of Lie type

Hiss, G. and Lübeck, F. and Malle, G., The Brauer trees of the exceptional Chevalley groups of type E6, Manuscripta Math., 87, (1995), p. 131--144

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

Hiss, G. and Lübeck, F., The Brauer trees of the exceptional groups of type F4 and 2E6, Arch. Math. (Basel), 70, (1998), p. 16--21

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

Here we use the explicit computation of some character values which allow to determine some multiplicities of irreducible representations in certain tensor products.

Generation of simple groups

Lübeck, F. and Malle, G., (2,3)-generation of exceptional groups, J. London Math. Soc., 59 (2), (1999), p. 109--122

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

Each simple exceptional group of Lie type is generated by an element of order two together with an element of order three. In our proof we use some explicit character values of these groups and information about their maximal subgroups.

Kemper, G., Lübeck, F. and Magaard, K., Matrix generators of the Ree groups 2G2(q), Comm. Algebra, 29 (1)(2001), p. 407--413

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

We also give generators of certain subgroups. Here are the matrices from the paper in Maple readable format.

Constructive recognition of groups

Lübeck, F., Magaard, K. and O'Brien, E.A. Constructive Recognition of SL3(q), J. Algebra, 316 (2007), p. 619--633

We describe an algorithm for constructing an isomorphism from a group isomorphic to SL3(q) in any (black box) representation to the natural representation as 3x3-matrices, such that elements can be mapped in both directions.

[BibTeX-Entry] [dvi-file (with hyperlinks)] [postscript-file] [pdf-file] (electronic reprint of published article available upon request)

Lübeck, F., Niemeyer, A. C. and Praeger, C. E. Finding involutions in finite Lie type groups of odd characteristic, J. Algebra, 321 (2009), p. 3397--3417

We estimate the proportion of elements of even order 2k in groups of Lie type whose k-th power is an involution with a prescribed structure of its centralizer.

[BibTeX-Entry] [preprint, linked pdf] [reprint, pdf, "Article in Print" version]

Representations of small degree

Lübeck, F., Smallest degrees of representations of exceptional groups of Lie type, Comm. Algebra, 29 (5) (2001), p. 2147--2169

[BibTeX-Entry] [dvi-file (with hyperlinks)] [postscript-file] [pdf-file]

The first few smallest degrees of projective complex representations of all exceptional simple groups of Lie type are given. Some information on modular representations in non-defining characteristic can be found as well.

Lübeck, F., Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math., 4 (2001), p. 135--169

(This is a slightly updated preprint version of January 2016, where a mistake in a statement about Frobenius-Schur indicators is corrected.)

[BibTeX-Entry] [pdf-file]

For all simple finite groups of Lie type we give a list of smallest degrees of representations in defining characteristic (e.g., up to degree 300 for type B2, 100000 for type E8 and for groups of large Lie rank l up to a degree proportional to l3).

Here are additional tables of weight multiplicities for the representations from this paper.

Tensor products of characters

Hiss,G. and Lübeck, F., Some observations on products of characters of finite classical groups, Proceedings of Finite Groups 2003, Gainesville (FL), in honor of J. G. Thompson's 70th birthday, de Gruyter (2004)

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

The experimental data used in this paper are available here.

Proportions of elements with certain orders in finite groups of Lie type

Guralnick, R. M. and Lübeck, F., On p-singular elements in Chevalley groups in characteristic p, Proceedings of Computational Group Theory, Columbus, Ohio, June 1999, de Gruyter, (2001)

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

An upper bound for the proportion of p-singular elements in finite Chevalley groups in characteristic p.

Lübeck, F., Finding p'-elements in finite groups of Lie type, Proceedings of Computational Group Theory, Columbus, Ohio, June 1999, de Gruyter, (2001)

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

A lower bound for the proportion of semisimple elements of order divisible by m in finite groups of Lie type.

Elementary divisors of integer matrices

Lübeck, F., On the Computation of Elementary Divisors of Integer Matrices, J. Symbolic Comput., 33 (2002), p. 57-65

[BibTeX-Entry] [dvi-file] [postscript-file] [pdf-file]

The main algorithm here is particularly powerful when the prime divisors of the determinant are known in advance. There is a GAP package EDIM containing implementations of most algorithms mentioned in the paper.

Orbit algorithm, direct condensation and parallelization

Lübeck, F. and Neunhöffer, M., Enumerating large orbits and direct condensation, Experiment. Math., Vol. 10, Number 2 (2001)

[BibTeX-Entry] [dvi-file (with hyperlinks)] [postscript-file] [pdf-file]

An implementation of the parallelized algorithm described in this paper can be found here.

Last updated: Wed Feb 28 19:12:06 2024 (CET)