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CHEVIE – A system for computing and processing generic character tables. (English) Zbl 0847.20006
This paper contains a survey on the capabilities of the computer algebra package CHEVIE which has been developed by the authors during the past few years. CHEVIE is based on the computer algebra systems GAP and MAPLE and consists of a library of data and programs for dealing with generic character tables of finite groups of Lie type and related structures.
It turns out that CHEVIE is a major contribution to computational Lie theory as well as to character theory of Chevalley groups. Moreover it has a wide range of applications in such different fields like (real and complex) reflection groups, representation theory of Iwahori-Hecke algebras, constructive Galois theory and knot theory.
The paper gives an introduction into the main features of CHEVIE. It describes in detail the used data types and most of the procedures and algorithms that are available. It also includes some examples of running times on standard machines which give the impression of a very efficient platform for doing highly nontrivial calculations.
CHEVIE can be obtained via anonymous ftp through ftp.math.rwth-aachen.de or ftp.iwr.uni-heidelberg.de and takes about 6 MegaByte of disc space.

MSC:
20C40 Computational methods (representations of groups) (MSC2010)
20C33 Representations of finite groups of Lie type
68W30 Symbolic computation and algebraic computation
Software:
CHEVIE; Maple; Coxeter; GAP
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