Frank Lübeck

Online Data - Overview

Here I give Web access to various kinds of mathematical data which I have computed or collected from the literature. By and by I will add new topics. For example I will provide many data concerning groups of Lie type, emphasizing the exceptional types.

Tell me (Email) if you are particularly interested in specific data. This could influence my priority list.

It is not obvious how large amounts of data are presented most conveniently. Suggestions for improvements of the presentation are also welcome.

Groups of Lie Type and Reductive Algebraic Groups

This section provides data related to finite groups of Lie type and their corresponding algebraic groups, in particular their conjugacy classes, subgroups and representations.

Conway Polynomials

This section contains a list of all known Conway polynomials which provide a standard notation for finite field elements. The majority of the given polynomials goes back to a list computed by R.Parker. But there are also many new ones computed recently with a parallel program written by me. The list will be extended as new polynomials are computed.

Gram Matrices for Specht Modules

Specht modules are irreducible modules for finite symmetric groups. There is a natural bilinear form defined on these modules. This section contains a collection of examples describing the elementary divisors of the corresponding Gram matrices.

All modules of dimension < 11700 are considered. Furthermore, in many cases the structure of the Jantzen filtrations follows from these results together with the knowledge on decomposition numbers.

Examples of Matrix Groups

Here are some examples of matrix groups over finite fields, created by Jürgen Müller and me. Everybody is invited to meet the challenge to find out as much as possible about the given groups.

Last updated: Fri Jul 23 14:24:49 2004 (CET)