[GAP Forum] Fwd: Herbert Pahlings

[Joachim Neubüser]

Dear colleagues,

I am very sad that I have to inform you of the death of Prof. Dr. 
Herbert Pahlings on January 9, 2012.
He is survived by his wife, whom he met already during his student time, 
his three sons and six grandchildren, to all of whom we would like to 
express our deepest sympathy.

Personally, I will always remember with gratitude the many years of our 
close, friendly and fruitful collaboration at Lehrstuhl D für 
Mathematik, RWTH Aachen, and I think we all  remember him with gratitude 
for his valuable contributions to computational group theory and to GAP 
in particular.

Herbert Pahlings was born on May 12, 1939 at Krefeld (Germany), he 
studied mathematics at the universities  of Tübingen and Gießen, where 
in 1968 he got his PhD for his thesis 'Beiträge zur Theorie der 
projektiven Darstellungen endlicher Gruppen'. His advisor was Professor 
Hermann Boerner. Since 1965 he  worked as an assistant at the department 
of mathematics at Gießen, interrupted by visits  in  1968  to  Texas A & 
M, and in 1973/74 to Carleton University, Ottawa, Canada. In 1975 he got 
his Habilitation and a permanent position as Akademischer Oberrat at 
Gießen until in 1979 he was appointed to a professorship at Lehrstuhl D 
für Mathematik.

Until his retirement in 2004 he had lectured at all levels, from 
beginners courses on Linear Algebra with an audience of several hundred 
students  to a broad spectrum of special courses, mainly on algebraic 
topics, in particular from group theory and representation theory. His 
lectures contained a wealth of material, often enriched in a very 
original way by his own ideas.  They  were loved and esteemed by the 
students for the clarity of their design and presentation. No wonder 
that he attracted many of the best students to work under his advice for 
their Diploma or even PhD. Of his PhD students Meinolf Geck, Klaus Lux, 
Götz Pfeiffer and Jürgen Müller meanwhile teach at universities while 
Thomas Breuer played and is playing a main role in the development of 
GAP and the construction of its representation theoretic data bases.

Herbert Pahling's papers from his time at Gießen deal with a variety of 
(often  concrete) problems from the representation theory of finite
groups. Also from this time there are lecture notes on modular 
representation theory of a course he gave at Istanbul in 1973. But it 
was only when he moved to Aachen that he soon developed a keen interest 
in algorithmic methods of representation theory, their implementation 
and use. He participated very actively in the development and use of a 
special program system CAS (Character Algebra System),  which he 
describes (together with coauthors)  in a paper published in the 
proceedings of a conference on Computational Group Theory held at Durham 
in 1982. The highlight of the paper were some worked-out examples 
provided by Herbert Pahlings. They show how new character tables could 
be obtained from (parts of) known ones  interactively using CAS without 
ever touching the elements of the underlying groups.

At that time  the classification of the finite simple groups had just 
been finished  and the preparation of the 'Atlas of Finite Groups' was 
on the way. Character tables of simple and related groups are a dominant 
feature of the Atlas and programs such as the ones of CAS were welcome 
in particular for interactive handling the character tables of groups by 
far too big for working from their elements. In the preface of the Atlas 
John Conway recognized the help obtained from Herbert Pahlings and the 
CAS group both by providing additional tables and correcting errors that 
are unavoidable in working 'by hand' with such a huge amount of data.

CAS was still written in Fortran and had a language suitable for 
interactive handling but not really for implementing new algorithms, so 
in 1986 we decided to start GAP (Groups, Algorithms and Programming) as 
a new system in which only basic time-critical functions were written in 
C while an own problem-adapted language should serve both as the user 
language and for implementation of mathematical algorithms. Herbert 
Pahlings patiently and constructively took part in the long discussions 
on the design of GAP and together with his students became a main 
developer and frequent and successful user of GAP. Several of his papers 
from his time in Aachen deal with applications to topics studied 
elsewhere: e.g. he contributed to the project of realizing finite groups 
as Galois groups  and there are papers on the Möbius function of groups.

Herbert Pahlings has spread the knowledge on computational 
representation theory by lectures and complete courses given at many 
places, e.g. in Brasil, South Africa, Ireland, Hungary and Italy (there 
are lecture notes of some of these courses) and was a splendid host for 
many visitors who came to Aachen to learn about this topic. He also 
served as a member of the GAP Council from 1995 to 2007, and as such had 
been  editor for the formal acceptance of several GAP packages.

Herbert Pahlings'  former students and colleagues have taken part in the 
publication of several collections of data connected with group 
representations: Gerhard Hiß and Klaus Lux published 'Brauer Trees of 
Sporadic Groups' in 1989, Christoph Jansen and Klaus Lux together with 
Richard Parker and Robert Wilson 'An Atlas of Brauer Characters' in 1995 
(which also contains corrections and addenda to the 'Atlas'), and Thomas 
Breuer 'Characters and Automorphism Groups of Compact Riemann Surfaces' 
in 2000.
*
*In 2010 Herbert Pahlings together with his former student Klaus Lux 
published 'Representations of Groups, A Computational Approach', a book
of 460 pages which in more than one way breaks new ground. It is the 
first text presenting a full view of algorithmic methods in both 
ordinary and modular representation theory, thus closing a strongly felt 
gap in the available literature on computational group theory. Moreover 
rather than relying on other texts for the theoretical background it 
builds up from scratch the theorems together with the algorithms, and it 
demonstrates the use of algorithms by  worked examples using GAP 
implementations. Thus it gives an example and a guideline for everybody 
planning a course on some algebraic structure for which not only 
theorems but also algorithms are known.

We will strongly miss Herbert Pahlings but we should be grateful for all 
he has given us.


Joachim Neubüser