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
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